Early Modern Science Research Articles

A historical analysis of the independent development of calculus by Newton and Leibniz

This paper undertakes a historical investigation of the separate and independent development of calculus by Isaac Newton and Gottfried Leibniz in the late 17th century. Through analysis of primary sources and historiographical perspectives, it explores the differences in notation, methods, and applications used by each mathematician to formulate foundational concepts of calculus. The research demonstrates that Newton relied more on geometric intuition, developing calculus concepts like fluxions and fluents rooted in kinematic problems. His 1687 Philosophiae Naturalis Principia Mathematica synthesized many calculus innovations. Meanwhile, Leibniz approached calculus from an algebraic mindset, utilizing infinitesimal differentials and comprehensively explaining integral and differential calculus in publications like Nova Methodus pro Maximis et Minimis. Evaluation of letters and documents from the 1670s and 1680s shows no direct collaboration or communication about calculus between Newton and Leibniz. This lack of transmission, coupled with the disparities in their notation and calculus techniques, provides evidence for independent creation. However, Newton and Leibniz shared key insights regarding rates of change, derivatives and integrals, hinting at a broader zeitgeist in early modern mathematics and science. Thus, this dual achievement illustrates how the Scientific Revolution facilitated conceptual convergence despite geographic separation between great thinkers. Investigating this case study offers perspective on the interplay between individual genius and wider social contexts in driving scientific progress. This paper concludes by assessing the legacy of the Newton-Leibniz debate over priority and analyzing work that paved the way for modern unified calculus notation and applications.

:Possible Knowledge: The Literary Forms of Early Modern Science

:<i>Possible Knowledge: The Literary Forms of Early Modern Science</i>

Pierre Gassendi: Humanism, Science, and the Birth of Modern Philosophy

Pierre Gassendi: Humanism, Science, and the Birth of Modern Philosophy

Early Modern Art and Science: Simulation of Dissections in the 16th Century Fugitive Sheets

During the 15th century the study of anatomy became a part of art education. With the rise of anatomy as a branch of medicine, artists began to play an important role in the process of anatomical research, creating graphic representations that served as powerful transmitters of knowledge. Among these, the most exquisite were anatomical fugitive sheets, the volumetric, three-dimensional representations of human anatomy. The layering, overlapping, of human organs, enabling one to manipulate them according to need, serves as simulation of the strategies of opening of human body during anatomical dissections. The artists-illustrators of these processes introduced new didactic interactive methods into acquisition and transfer of knowledge. In close cooperation with scientists, they found ways to translate information into recognizable and accessible models, endowing them with cognitive structure, as in anatomical atlases by Andrea Vesalius, De humani corporis fabrica (1543), and Johann Remmelin, Catoptri Microcosmici (1609).

Naturalism in the Christian Imagination: Providence and Causality in Early Modern England

Naturalism in the Christian Imagination: Providence and Causality in Early Modern England

More-than-Human Wellbeing

More-than-Human Wellbeing

Special Issue Introduction: Individuality, Self-Care, and Self-Preservation in Late Medieval and Early Modern Science

Special Issue Introduction: Individuality, Self-Care, and Self-Preservation in Late Medieval and Early Modern Science

Astrological Self-Government at the Fifteenth-Century Court of Bourbon

Abstract In articulating the uses of their art, late-medieval astrologers often invoked the maxim that “the wise man will rule the stars” (sapiens dominabitur astris). However, it is by no means clear whether this invocation sought to emphasize ‘domination’ over the natural and social world, or the ontological self-government that is at stake in the pursuit of ‘wisdom’. Many historians have interpreted the past pursuit of astrology in terms of an interest in dominance over the natural and social world. Taking inspiration from a recent ‘ascetic turn’ in the history of early modern science and philosophy, however, this article argues that late-medieval astrology was approached and appreciated as an art of self-government (both in body and in soul) and uncovers what this entailed. In so doing, we also demonstrate that the undifferentiated view of astrology as a pre-modern counterpart of modern prospective knowledge practices is anachronistic.

Diverse Shapes: Used Goods as Material Resources in Early Modern Sciences

Diverse Shapes: Used Goods as Material Resources in Early Modern Sciences

The Cutting Edge in Print

This article explores how Scholastic notions of the body, mind and cognition inform the didactic principles structuring the Opera nova (1536) by Achille Marozzo (1484-1553). A Bolognese fencing master, Marozzo belonged to a tradition of institutionalized martial training which had historically emphasized its connections to academic discourses of learning. In spite of this, Marozzo’s own work has been interpreted as following a straightforward tradition of copying forms and patterns, without much of an underlying theoretical argument. This article argues that Marozzo does present several conceptual references to Scholastic ideas about the workings of the brain, however, in particular to the mind’s dependence on mental images provided by the senses. Delving into these references not only helps to understand the didactic principles at work in the Opera nova as a whole, but also the specific role Marozzo seems to have attributed to the many woodcuts included in his book. In presenting this argument, this article then argues for the fruitful insights that can be gained from connecting fight books to both medieval and early modern Scholasticism, and the history of early modern art and science.

New Books across the Disciplines

New Books across the Disciplines

“Ícaros de discursos racionales”: The Comet of 1680–1681, Sor Juana’s Neptuno alegórico, and the Enduring Function of Myths in an Age of Enlightenment

Abstract Stark differences have been noted in the ways Sor Juana Inés de la Cruz and Carlos de Sigüenza y Góngora responded in 1680 to the arrival in New Spain of both a new viceroy as well as a great comet. Such comparisons have tended to hinge on the question of which of the two colonial Spanish-American writers was more “modern” versus “traditional.” Such valuative contrasts between Sor Juana and Sigüenza y Góngora implicitly evoke a commonplace but erroneous historical narrative that privileges the advent of modern science at the expense of poetry and myth. It is by acknowledging the shared affective goal of myth and early modern science in regulating human fears of natural forces, as Hans Blumenberg has done, that scholars can better assess the enduring function of Neptune for a poet like Sor Juana in an Age of Enlightenment. This reappraisal of myth’s function permits in turn a more dialogic reading of Sor Juana and Sigüenza y Góngora’s respective arches and their shared Neptunian response to the debates that raged in seventeenth-century Mexico City over flood control efforts and the value of indigenous hydraulic knowledge. In this reading, Neptune represents a European mythographic discourse of power over nature that serves to both assuage criollo fears of flooding while also displacing the challenge posed by indigenous hydraulic knowledge to Spanish intellectual hegemony in New Spain in part by replacing the Mexica god Tlaloc with Neptune.

Lady Ranelagh’s contributions to early modern science

Lady Ranelagh’s contributions to early modern science

The Infrastructure of Science Making in Early Modern China

Abstract In the early modern era China witnessed an explosive growth in discourse regarding things known as bowu. In some ways resembling the study of natural history in Europe, it was oriented toward the strange and exotic. A renowned bowu master, Xie Zhaozhe left behind prolific writings on the subject, recording not only the natural historical knowledge he amassed but also how he produced that knowledge. Using Xie as an empirical case, this article proposes a model for an “infrastructure of science making” with which to conceptualize early modern Chinese science as a situated knowledge. It explores the profiles of Xie’s book learning, of his real-world encounters with natural phenomena through praxis, and of his collaboration and exchange with other members of his discursive community. An in-depth examination of these parameters in his knowledge infrastructure raises some salient points for understanding the broader trends in natural studies in early modern China and the wider early modern world.

The ‘system of the world’ and the scientific culture of early modern France

Historians have long debated the origins of modern science in early modern Europe. Recently, however, scholars pointed to our need to understand how the ‘new philosophy’ became a sustained movement, which did not dissipate over the course of a few generations, as had previous scientific renaissances in other civilizations. This article suggests that the mediations of the printed book allowed a broader public to engage with the astronomical ideas at the core of scientific transformations. This article examines the interactions that the world of the book generated between authors at the ‘core’ of early modern science and ‘amateurs’ who were interested in recent cosmological discussion around the notion of the ‘system of the world’. It argues that this concept served simultaneously to discuss mathematico-physical problems, to make claims for authorship and to provide cultural orientation, which made it amenable to appropriation and dialogue across a range of genres. The new social interactions around the ‘system of the world’ allowed a heavily mathematical science to become a viable and sustainable cultural phenomenon, a veritable building-block of a new scientific culture at the heart of European modernity.

New Books across the Disciplines

New Books across the Disciplines

The Body in History, Culture, and the Arts

The Body in History, Culture, and the Arts

“Trust No One But Yourself”: William Gilbert’s Use of Experiment and Rejection of Authority, Reconsidered

Abstract One of the most important components of early modern science was the experiment. Advocates of the “new sciences” used experiments as indisputable evidence in controversies with their opponents and as powerful arguments against authoritative texts. Among the first early modern scientific works to systematically and successfully use experiments as parts of the central argumentation is William Gilbert’s treatise De magnete (1600), in which the author sought to present a completely new theory of magnetism as an explanation of phenomena on earth as well as of the movements of heavenly bodies. Gilbert goes to great lengths to persuade his readers of the innovation of his nova et inaudita physiologia. For this, however, it did not suffice to present a startling number of experiments and advocate empirical investigation. This contribution will shed light on the surprising literary and rhetorical tools employed in the De magnete in questions of authority, which aided Gilbert in presenting his powerful and highly successful “New Physiology.”

Introduction: Science and connoisseurship in the European Enlightenment.

A major theme of the European Enlightenment was the rationalization of value, the use of reason to determine the value of things, from diamonds to civilizations. This view of the Enlightenment is well-established in the human sciences. It is ripe for extension to the natural sciences, given the rich recent literature on affect, evaluation, and subjectivity in early modern science. Meanwhile, in art history, the new history of connoisseurship provides a model for the historical study of the evaluation of material things. Historians of natural history have already noted the connections between science, Enlightenment, and connoisseurship. The time has come to extend their insights to other areas of Enlightenment science. This means recognizing the breadth of connoisseurship - the social, linguistic, and disciplinary diversity of the practice - as understood in Europe in the eighteenth century and the latter part of the seventeenth century. An outline of the three papers in this special section gives an indication of how this historiographical project might be carried out.

Cura, the Curatorial and Paradoxes of Care

Drawing on the classical myth of the goddess Cura, I show that care is concerned with the temporality of Being, a feeling for time in tension between the desire for a world that endures despite our mortality whilst also constantly open to our innate capacity for originality. I elaborate this proposition through its intimate and ambivalent relationship with its counterpart, security, and especially through the topos of the curator. The latter’s deployment and simplifications through time, implicitly tasked with removing worries and cares, disavow the paradoxes that comprise its morphology. From its emergence with the Roman Empire, I attend to its resonances within the curacy of the Catholic Church, its transformation with the Reformation and the natural theology of early modern science, its transference to the museum as one responsible for preserving and generating historical understanding, and its more recent re-fashioning as a technique for producing and performing self-identity through selection. The current ubiquity of curation beyond the museum and gallery can be understood, I suggest, not as an aberration but perhaps as a symptom of our temporal malaise, the pathology and felt exhaustion of a stalled project of modernity for which we have been repeatedly told ‘there is no alternative’. I conclude by briefly considering some of the implications of accepting the complexities of care and curation for affecting temporal experience without reproducing the logic that sustains our current impasse.