I. Bernard Cohen

Hypotheses in Newton’s Philosophy

Isaac Newton’s scientific thought is all too often presented as if it had been dominated by a single philosophical slogan: Hypotheses non fingo! The scholars who have applied this expression to all Newton’s writings evidently take as axiomatic that Newton’s stand on hypotheses never changed from the early period of 1672, when Newton published his first paper on color, to 1712, when he wrote out the General Scholium for the second edition of the Principia, and in it imbedded those three famous words about hypotheses. But such a supposed constancy of Newton’s views will surely appear astonishing to anyone who is acquainted with the development of thought in so long a span (some 40 years) in the creative life of a reflecting scientist like Newton!

‘Quantum in Se Est’ : Newton’s concept of inertia in relation to Descartes and Lucretius

Every now and then in the study of the development of science, a single sentence or a phrase may yield a key to the deep recesses of the creative scientific mind. Such a phrase is quantum se est, displaying to us in a novel and dramatic way the hidden roots of one of Isaac Newton’s major concepts that might otherwise have escaped our scholarly attention. The phrase itself, quantum in se est, rings with a cadence that may seem more appropriate to a publication devoted to classical philology or medieval philosophy than to these Notes and Records. Let me say at the outset, therefore, that this phrase comes from Newton’s Principia, the greatest by far of the first works to issue from the press with the imprimatur of the Royal Society. In the Principia, as we shall see, this expression is prominently and somewhat perplexingly displayed in relation to the initial physical axiom of that work, the Law of Inertia.

Makin' numbers: Howard Aiken and the computer

with the cooperation of Robert V. D. CampbellThis collection of technical essays and reminiscences is a companion volume to I. Bernard Cohens biography, Howard Aiken: Portrait of a Computer Pioneer. After an overview by Cohen, Part I presents the first complete publication of Aikens 1937 proposal for an automatic calculating machine, which was later realized as the Mark I, as well as recollections of Aikens first two machines by the chief engineer in charge of construction of Mark II, Robert Campbell, and the principal programmer of Mark I, Richard Bloch. Henry Tropp describes Aikens hostility to the exclusive use of binary numbers in computational systems and his alternative approach.Part II contains essays on Aikens administrative and teaching styles by former students Frederick Brooks and Peter Calingaert and an essay by Gregory Welch on the difficulties Aiken faced in establishing a computer science program at Harvard. Part III contains recollections by people who worked or studied with Aiken, including Richard Bloch, Grace Hopper, Anthony Oettinger, and Maurice Wilkes. Henry Tropp provides excerpts from an interview conducted just before Aikens death. Part IV gathers the most significant of Aikens own writings. The appendixes give the specs of Aikens machines and list his doctoral students and the topics of their dissertations.

Newton’s Third Law and Universal Gravity

Newton’s great Principia is doubly tripartite. It is composed of three “books” and has three major goals: to set forth new foundations and methods of rational mechanics; to disclose a new natural philosophy; and to develop a new system of the world based on gravitational celestial dynamics. Attention shall be focussed here on the crucial step that enabled Newton to develop and to use the concept of universal gravity and to state its quantitative law. A plausible explanation shall be offered for Newton’s daring in proposing a universal force that could extend over hundreds of millions of miles of empty space, a kind of force that in its basic properties went squarely against the principles of the “received” mechanical philosophy.1

The Principia, Universal Gravitation, and the “Newtonian Style”, in relation to the Newtonian Revolution in Science:

Scholars generally agree that Newton’s Principia marks the climax of the Scientific Revolution.1 This great treatise epitomized the application of mathematics to natural philosophy and set a standard which scientists in such diverse areas as palaeontology and physical chemistry saw as the goal for all developing sciences.2 Yet, to judge from the current literature in intellectual history, the history of philosophy, and even the general history of science, and despite the unanimity on the importance of Newton’s Principia, there is a rather wide-spread lack of precision and a considerable variation from one author to another regarding the nature of the book — its contents, its method, its positive accomplishments, and its failures. Very few scholars today, save for Newtonian specialists, have read the Principia through from cover to cover — a task that demands mathematical skills beyond the range of most historians, plus a background in various aspects of physics and of celestial mechanics.3 Newton himself was aware of the fact that to study carefully every proposition of the first two books of the Principia ‘might be too time-consuming even for readers who are learned in mathematics’, and so he said that he was ‘unwilling to advise anyone to study every one of these propositions’.4

An Analysis of Interactions between the Natural Sciences and the Social Sciences

Ever since the time of Aristotle, the natural sciences and medicine have furnished analogies for studies of governments, classifications of constitutions, and analyses of society.* One of the fruits of the Scientific Revolution was the vision of a social science — a science of government, of individual behavior, and of society — that would take its place among the triumphant sciences, producing its own Newtons and Harveys. The goal was not only to achieve a science with the same foundations of certain knowledge as physics and biology; there was thought to be a commonality of method that would advance the social sciences in the way that had worked so well in the physical and biological sciences. Any such social science, it was assumed, would be based on experiments and critical observations, would become quantitative, and would eventually take the highest form known to the sciences — expression in a sequence of mathematical equations.

The Isis Crises and the Coming of Age of the History of Science Society

ANYONE WHO EXAMINES THE DEVELOPMENT of the History of Science Society I (HSS) will note a sharp cleavage between its activities and institutional structure in the years before and after World War II. In part this was caused by the postwar growth of the history of science as an academic discipline that eventually required an infrastructure adapted to the new professional needs. But the precipitating factor that completely altered the character of the HSS was the response to a series of problems that arose in relation to the publication of Isis. In this presentation I shall deal, first of all, with these problems of publishing Isis and then turn to the growth of the profession of History of Science and the constantly expanding role of the HSS.

The Scientific Revolution and the Social Sciences

Ever since the great revolution which produced modern science there has been a hope that a science of society would be created on a par with the sciences of nature. Two early heroes of the Scientific Revolution, Galileo and Harvey, created radical transformations of science — respectively, a physics of motion and a physiology based on the circulation of the blood — which became paradigms for a new social science.1 Scientific precepts of Bacon and of Descartes were available as guides in this new venture. A primary challenge was to accommodate a new social science to mathematics: either to use classical mathematics for a non-traditional purpose or to introduce a kind of mathematics other than geometry on the Greek pattern. Would-be social scientists could thus find novel ways of dealing with their subject that would transfer to their endeavors the authority of mathematics and the new natural sciences.

William Whewell and the Concept of Scientific Revolution

Discussions of scientific change have, in recent years, come to center more and more on the concept of scientific revolution. No doubt, one of the reasons for the attention given to scientific revolutions has been the challenging thesis of Thomas S. Kuhn, in his widely-read book, The Structure of Scientific Revolutions.2 The critical response to Kuhn’s book3 has largely been of three kinds: criticising his fundamental thesis or some aspect of it,4 challenging the propriety of using the concept of revolution in the analysis of scientific change,5 and substituting an alternative schema for our understanding of the development of science.6 But no one thus far has seriously taken on the assignment of tracing the origin and vicissitudes of development of the concept and name ‘revolution’ as it has been applied to specific changes in the sciences (as in the Copernican, Newtonian, and Darwinian revolutions)7 or to large-scale changes that have affected science as a whole and man’s views of himself, his universe, and nature. Many historians appear to believe that it is only in very recent years that the concept of revolution has become imposed harshly and anachronistically on the scientific events of the past. Accordingly, there is a special relevance to exploring the history of the successive attempts to explain scientific change by revolutions.

Isaac Newton, The Calculus of Variations, and the Design of Ships

Mathematical and sociological judgment concurs in the belief that the Principia shows how Newton developed pure science for a practical purpose. In particular, the way in which “the problem of ship design led Newton to the calculus of variations”1 would appear to be evidence of the social roots of scientific innovation in the seventeenth century. Newton’s statement is brief. He has been comparing different shapes or figures of solids of revolution as to their resistance, under certain given conditions, to being moved; then he says, only, “This proposition I conceive may be of use in the building of ships.”2