This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and (...) made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

Roughly speaking, classical statistical physics is the branch of theoretical physics that aims to account for the thermal behaviour of macroscopic bodies in terms of a classical mechanical model of their microscopic constituents, with the help of probabilistic assumptions. In the last century and a half, a fair number of approaches have been developed to meet this aim. This study of their foundations assesses their coherence and analyzes the motivations for their basic assumptions, and the interpretations of their central concepts. (...) The most outstanding foundational problems are the explanation of time-asymmetry in thermal behaviour, the relative autonomy of thermal phenomena from their microscopic underpinning, and the meaning of probability. A more or less historic survey is given of the work of Maxwell, Boltzmann and Gibbs in statistical physics, and the problems and objections to which their work gave rise. Next, we review some modern approaches to (i) equilibrium statistical mechanics, such as ergodic theory and the theory of the thermodynamic limit; and to (ii) non-equilibrium statistical mechanics as provided by Lanford's work on the Boltzmann equation, the so-called Bogolyubov-Born-Green-Kirkwood-Yvon approach, and stochastic approaches such as `coarse-graining' and the `open systems' approach. In all cases, we focus on the subtle interplay between probabilistic assumptions, dynamical assumptions, initial conditions and other ingredients used in these approaches. (shrink)

Pierre de Fermat is known as the inventor of modern number theory. He invented–improved many methods useful in this discipline. Fermat often claimed to have proved his most difficult theorems thanks to a method of his own invention: the infinite descent. He wrote of numerous applications of this procedure. Unfortunately, he left only one almost complete demonstration and an outline of another demonstration. The outline concerns the theorem that every prime number of the form 4n + 1 is the sum (...) of two squares. In this paper, we analyse a recent proof of this theorem. It is interesting because: it follows all the elements of which Fermat wrote in his outline; it represents a good introduction to all logical nuances and mathematical variants concerning this method of which Fermat spoke. The assertions by Fermat will also be framed inside their historical context. Therefore, the aims of this paper are related to the history of mathematics and to the logic of proof-methods. (shrink)

The mathematical theory of communication.

Thomas S. Kuhn's classic book is now available with a new index.

This book offers insights relevant to modern history and epistemology of physics, mathematics and, indeed, to all the sciences and engineering disciplines emerging of 19th century. This research volume is the first of a set of three Springer books on Lazare Nicolas Marguérite Carnot’s (1753–1823) remarkable work: Essay on Machines in General (Essai sur les machines en général [1783] 1786). The other two forthcoming volumes are: Principes fondamentaux de l’équilibre et du mouvement (1803) and Géométrie de position (1803). Lazare Carnot (...) – l'organisateur de la victoire – in Essai sur le machine en général (1786) assumed that the generalization of machines was a necessity for society and its economic development. Subsequently, his new coming science applied to machines attracted considerable interest for technician, as well, already in the 1780’s. With no lack in rigour, Carnot used geometric and trigonometric rather than algebraic arguments, and usually went on to explain in words what the formulae contained. His main physical– mathematical concepts were the Geometric motion and Moment of activity–concept of Work . In particular, he found the invariants of the transmission of motion (by stating the principle of the moment of the quantity of motion) and theorized the condition of the maximum efficiency of mechanical machines (i.e., principle of continuity in the transmission of power). While the core theme remains the theories and historical studies of the text, the book contains an extensive Introduction and an accurate critical English Translation – including the parallel text edition and substantive critical/explicative notes – of Essai sur les machines en général (1786). The authors offer much-needed insight into the relation between mechanics, mathematics and engineering from a conceptual, empirical and methodological, and universalis point of view. As a cutting–edge writing by leading authorities on the history of physics and mathematics, and epistemological aspects, it appeals to historians, epistemologist–philosophers and scientists (physicists, mathematicians and applied sciences and technology). (shrink)

To commemorate the 50th anniversary of his passing, this special book features studies on Alexandre Koyré, one of the most influential historians of science of the 20th century, who re-evaluated prevalent thinking on the history and philosophy of science. In particular, it explores Koyré’s intellectual matrix and heritage within interdisciplinary fields of historical, epistemological and philosophical scientific thought. Koyré is rightly noted as both a versatile historian on the birth and development of modern science and for his interest in philosophical (...) questions on the nature of scientific knowledge. In the 1940s and 1950s his activities in the United States established a crucial bridge between the European historical tradition of science studies and the American academic environments, and an entire generation of historians of science grew up under his direct influence. The book brings together contributions from leading experts in the field, and offers much-needed insights into the subject from historical, nature of science, and philosophical perspectives. It provides an absorbing and revealing read for historians, philosophers and scientists alike. (shrink)

James Prescott Joule’s (1818–1889) bicentenary took place in 2018 and commemorated by the IDTC with a Symposium—‘James Joule’s Bicentenary: Scientific and Pedagogical Issues Concerning Energy Conservation’—at the European Society for the History of Science (ESHS & BSHS), 14th–17th September, 2018, in London. This symposium had three main objectives: It aimed specifically to celebrate James Joule’s achievements considering the most recent historiographical works with a particular focus on the principle of conservation of energy; It served the purpose of discussing the scientific (...) and pedagogical issues related to heat, energy and work and how they are presented in textbooks and worked out in classrooms; It also provided discussions on the present situation of teaching and learning science through the use of History of Science, both in K-12 and college level with an emphasis on energy and related concepts. In the following, the Introduction of this Special Issue on Joule is presented. (shrink)

In recent decades, the development of sciences and technologies had a significant impact in society. This impact has been object of analysis from several standpoints, i.e., scientific, communication, historical and anthropological. Consequently, serious changes were required by the society. One of these has been the emerging relationship science in society and its foundations of applied sciences. A related foundational challenging is the educational process, which was and still is an unlimited challenge for teachers and professors: i.e., levels of understanding, curricula, (...) activing critical engagement, transfer knowledge—and—skills, management, classroom and subsequently pre-service teachers need special teacher education. Taking into account Joule’s bicentenary commemoration in physics and Nature of Science teaching (NoS) this paper introduces to a level of inquiring within historical and NoS approaches in the pre-service teachers, typically science, technology, engineering and mathematics. In particular, history and historiography of Joule’s physics (e.g., his arguments on electric–magnetic engine, mechanical equivalent of heat and free expansion) are dealt with. (shrink)

In the history of science, the birth of classical chemistry and thermodynamics produced an anomaly within Newtonian mechanical paradigm: force and acceleration were no longer citizens of new cited sciences. Scholars tried to reintroduce them within mechanistic approaches, as the case of the kinetic gas theory. Nevertheless, Thermodynamics, in general, and its Second Law, in particular, gradually affirmed their role of dominant not-reducible cognitive paradigms for various scientific disciplines: more than twenty formulations of Second Law—a sort of indisputable intellectual wealth—are (...) conceived after 1824 Sadi Carnot’s original statement and a multitude of entropy functions are proposed after 1865 Clausius’ former definition. Furthermore, at the end of nineteenth century, thermodynamics extended its cognitive domain to chemistry. Mainly thanks to Gibbs, a brand new discipline—chemical thermodynamics or physical chemistry—gradually affirmed its role inside the scientific community. This paper reports the former results of collaborative research program in the History and Epistemology of Science as well as Nature of Science Teaching aimed at retracing the foundations of the physical chemistry. Specifically, the research is structured in three parts: historical-epistemic reflections on fundamental thermodynamic concepts and principles—such as reversible process, heat, temperature, thermal equilibrium and Clausius’ Second Law—that play a structural role inside modern physical chemistry; panoramic overview on the entropy, whose polysemy makes it one of the most demanding concepts for scholars, teachers and students while approaching thermodynamics; conceptualization of chemical equilibrium as complex entity according to the dual epistemological approach offered by Gibbs’ thermodynamic model and the kinetic standpoint by Guldberg and Waage. In particular, the present work details an original reading of thermodynamic principles with the aim of setting forth a rationalized multidisciplinary substrate whereon the foundational concepts of reversible process and thermal equilibrium can be set. (shrink)

In the history of science, the birth of classical chemistry and thermodynamics produced an anomaly within Newtonian mechanical paradigm: force and acceleration were no longer citizens of new cited sciences. Scholars tried to reintroduce them within mechanistic approaches, as the case of the kinetic gas theory. Nevertheless, Thermodynamics, in general, and its Second Law, in particular, gradually affirmed their role of dominant not-reducible cognitive paradigms for various scientific disciplines: more than twenty formulations of Second Law—a sort of indisputable intellectual wealth—are (...) conceived after 1824 Sadi Carnot’s original statement and a multitude of entropy functions are proposed after 1865 Clausius’ former definition. Furthermore, at the end of nineteenth century, thermodynamics extended its cognitive domain to chemistry. Mainly thanks to Gibbs, a brand new discipline—chemical thermodynamics or physical chemistry—gradually affirmed its role inside the scientific community. This paper reports the former results of collaborative research program in the History and Epistemology of Science as well as Nature of Science Teaching aimed at retracing the foundations of the physical chemistry. Specifically, the research is structured in three parts: historical-epistemic reflections on fundamental thermodynamic concepts and principles—such as reversible process, heat, temperature, thermal equilibrium and Clausius’ Second Law—that play a structural role inside modern physical chemistry; panoramic overview on the entropy, whose polysemy makes it one of the most demanding concepts for scholars, teachers and students while approaching thermodynamics; conceptualization of chemical equilibrium as complex entity according to the dual epistemological approach offered by Gibbs’ thermodynamic model and the kinetic standpoint by Guldberg and Waage. In particular, the present work details an original reading of thermodynamic principles with the aim of setting forth a rationalized multidisciplinary substrate whereon the foundational concepts of reversible process and thermal equilibrium can be set. (shrink)

James Prescott Joule’s (1818–1889) bicentenary took place in 2018 and commemorated by the IDTC with a Symposium—‘James Joule’s Bicentenary: Scientific and Pedagogical Issues Concerning Energy Conservation’—at the European Society for the History of Science (ESHS & BSHS), 14th–17th September, 2018, in London. This symposium had three main objectives: It aimed specifically to celebrate James Joule’s achievements considering the most recent historiographical works with a particular focus on the principle of conservation of energy; It served the purpose of discussing the scientific (...) and pedagogical issues related to heat, energy and work and how they are presented in textbooks and worked out in classrooms; It also provided discussions on the present situation of teaching and learning science through the use of History of Science, both in K-12 and college level with an emphasis on energy and related concepts. In the following, the Introduction of this Special Issue on Joule is presented. (shrink)

This paper is divided into two parts, this being the first one. The second is entitled ‘Historical and Epistemological Reflections on the Culture of Machines around Renaissance: Machines, Machineries and Perpetual Motion’ and will be published in Acta Baltica Historiae et Philosophiae Scientiarum in 2015. Based on our recent studies, we provide here a historical and epistemological feature on the role played by machines and machineries. Ours is an epistemological thesis based on a series of historical examples to show that (...) the relations between theoretical science and the construction of machines cannot be taken for granted, a priori. Our analysis is mainly based on the culture of machines around 15th and 17th centuries, namely the epoch of Late Renaissance and Early Modern Age. For this is the period of scientific revolution and this age offers abundant interesting material for researches into the relations of theoretical science/construction of machines as well. However, to prove our epistemological thesis, we will also exploit examples of machines built in other historical periods. Particularly, a discussion concerning the relationship between science theory and the development of science art crafts produced by non-recognized scientists in a certain historical time is presented. The main questions are: when and why did the tension between science give rise to a new scientific approach to applied discipline such as studies on machines and machineries? What kind of science was used for projecting machines and machineries? Was science at the time a necessary precondition to build a machine? In the first part we will focus on the difference between Aristotelian-Euclidean and Archimedean approaches and we will outline the heritage of these two different approaches in late medieval and Renaissance science. In the second part, we will apply our reconstructions to some historical and epistemological problems concerning the relations of science/technology/constructions of machines. The problem of perpetual motion will play an important role in this context. (shrink)

In recent decades, the development of sciences and technologies had a significant impact in society. This impact has been object of analysis from several standpoints, i.e., scientific, communication, historical and anthropological. Consequently, serious changes were required by the society. One of these has been the emerging relationship science in society and its foundations of applied sciences. A related foundational challenging is the educational process, which was and still is an unlimited challenge for teachers and professors: i.e., levels of understanding, curricula, (...) activing critical engagement, transfer knowledge—and—skills, management, classroom and subsequently pre-service teachers need special teacher education. Taking into account Joule’s bicentenary commemoration in physics and Nature of Science teaching this paper introduces to a level of inquiring within historical and NoS approaches in the pre-service teachers, typically science, technology, engineering and mathematics. In particular, history and historiography of Joule’s physics are dealt with. (shrink)

Forums, I extensively analysed Tartaglia’s corpus: science of weights, geometry, arithmetic, mathematics and physics–trajectories of the projectiles, fortifications, included its intelligibility science in the military architecture. The latter is exposed in Book VI of the Quesiti et invention diverse (hereafter Quesiti). In Quesiti there is La Gionta del sesto libro—a kind of appendix to the Book VI containing drawings of the geometric shape of the Italian fortifications. It is based on Euclidean geometry and other figures where a scale is displayed. (...) The interest—included intellectual history and cultural foundations of science—is: what is the role–played by La Gionta del sesto libro in the Quesiti? Is it independent booklet/speeches? If yes, when Tartaglia did write it? In this paper, I present an historical–philological–foundational hypothesis on the Tartaglia’s fortifications corpus, as exposed in the Book VI and La Gionta del sesto libro; with respect to dates of editions of Quesiti (1546, 1554). This goal is important to make historically clear both the editorial role–played by Curzio Troiano Navò (fl. 16th) in the Tartaglia’s corpus before—after Tartaglia’s death (1557) and the particular interest and development of subject of fortifications by Tartaglia between 1537–1546 and 1554. (shrink)

Forums, I extensively analysed Tartaglia’s corpus: science of weights, geometry, arithmetic, mathematics and physics–trajectories of the projectiles, fortifications, included its intelligibility science in the military architecture. The latter is exposed in Book VI of the Quesiti et invention diverse. In Quesiti there is La Gionta del sesto libro—a kind of appendix to the Book VI containing drawings of the geometric shape of the Italian fortifications. It is based on Euclidean geometry and other figures where a scale is displayed. The interest—included (...) intellectual history and cultural foundations of science—is: what is the role–played by La Gionta del sesto libro in the Quesiti? Is it independent booklet/speeches? If yes, when Tartaglia did write it? In this paper, I present an historical–philological–foundational hypothesis on the Tartaglia’s fortifications corpus, as exposed in the Book VI and La Gionta del sesto libro; with respect to dates of editions of Quesiti. This goal is important to make historically clear both the editorial role–played by Curzio Troiano Navò in the Tartaglia’s corpus before—after Tartaglia’s death and the particular interest and development of subject of fortifications by Tartaglia between 1537–1546 and 1554. (shrink)

Forums, I extensively analysed Tartaglia’s corpus: science of weights, geometry, arithmetic, mathematics and physics–trajectories of the projectiles, fortifications, included its intelligibility science in the military architecture. The latter is exposed in Book VI of the Quesiti et invention diverse. In Quesiti there is La Gionta del sesto libro—a kind of appendix to the Book VI containing drawings of the geometric shape of the Italian fortifications. It is based on Euclidean geometry and other figures where a scale is displayed. The interest—included (...) intellectual history and cultural foundations of science—is: what is the role–played by La Gionta del sesto libro in the Quesiti? Is it independent booklet/speeches? If yes, when Tartaglia did write it? In this paper, I present an historical–philological–foundational hypothesis on the Tartaglia’s fortifications corpus, as exposed in the Book VI and La Gionta del sesto libro; with respect to dates of editions of Quesiti. This goal is important to make historically clear both the editorial role–played by Curzio Troiano Navò in the Tartaglia’s corpus before—after Tartaglia’s death and the particular interest and development of subject of fortifications by Tartaglia between 1537–1546 and 1554. (shrink)

This book presents the life and personality, the scientific and philosophical work of Ludwig Boltzmann, one of the great scientists who marked the passage from 19th- to 20th-Century physics. His rich and tragic life, ending by suicide at the age of 62, is described in detail. A substantial part of the book is devoted to discussing his scientific and philosophical ideas and placing them in the context of the second half of the 19th century. The fact that Boltzmann was the (...) man who did most to establish that there is a microscopic, atomic structure underlying macroscopic bodies is documented, as is Boltzmann's influence on modern physics, especially through the work of Planck on light quanta and of Einstein on Brownian motion. Boltzmann was the centre of a scientific upheaval, and he has been proved right on many crucial issues. He anticipated Kuhn's theory of scientific revolutions and proposed a theory of knowledge based on Darwin. His basic results, when properly understood, can also be stated as mathematical theorems. Some of these have been proved: others are still at the level of likely but unproven conjectures. The main text of this biography is written almost entirely without equations. Mathematical appendices deepen knowledge of some technical aspects of the subject. (shrink)

The book presents the life and personality, the scientific and philosophical work of Ludwig Boltzmann, one of the great scientists who marked the passage from 19th to 20th century physics. His rich and tragic life, ending by suicide at the age of 62, is described in detail. A substantial part of the book is devoted to discussing his scientific and philosophical ideas and placing them in the context of the second half of the 19th century. The fact that Boltzmann was (...) the man who did most to establish that there is a microscopic, atomic structure underlying macroscopic bodies is documented, as is Boltzmann's influence on modern physics, especially through the work of Planck on light quanta and of Einstein on Brownian motion. Boltzmann was the centre of a scientific revolution, and he has been proved right on many crucial issues. He anticipated Kuhn's theory of scientific revolutions and proposed a theory of knowledge based on Darwin. His basic results, when properly understood, can also be stated as mathematical theorems. Some of these have been proved; others are still at the level of likely but unproven conjectures. The main text of this biography is written almost entirely without equations. Mathematical appendices deepen knowledge of some technical aspects of the subject. (shrink)

[Time, the fundamental dimension of our existence, has fascinated artists, philosophers, and scientists of every culture and every century. All of us can remember a moment as a child when time became a personal reality, when we realized what a "year" was, or asked ourselves when "now" happened. Common sense says time moves forward, never backward, from cradle to grave. Nevertheless, Einstein said that time is an illusion. Nature's laws, as he and Newton defined them, describe a timeless, deterministic universe (...) within which we can make predictions with complete certainty. In effect, these great physicists contended that time is reversible and thus meaningless. (shrink)

This book presents the concept of “complementary science” which contributes to scientific knowledge through historical and philosophical investigations. It emphasizes the fact that many simple items of knowledge that we take for granted were actually spectacular achievements obtained only after a great deal of innovative thinking, painstaking experiments, bold conjectures, and serious controversies. Each chapter in the book consists of two parts: a narrative part that states the philosophical puzzle and gives a problem-centred narrative on the historical attempts to solve (...) the puzzle; and the analysis part which provides in-depth analyses of certain scientific, historical, and philosophical aspects of the story. (shrink)

One may discuss the role played by mechanical science in the history of scientific ideas, particularly in physics, focusing on the significance of the relationship between physics and mathematics in describing mathematical laws in the context of a scientific theory. In the second Newtonian law of motion, space and time are crucial physical magnitudes in mechanics, but they are also mathematical magnitudes as involved in derivative operations. Above all, if we fail to acknowledge their mathematical meaning, we fail to comprehend (...) the whole Newtonian mechanical apparatus. For instance, let us think about velocity and acceleration. In this case, the approach to conceive and define foundational mechanical objects and their mathematical interpretations changes. Generally speaking, one could prioritize mathematical solutions for Lagrange’s equations, rather than the crucial role played by collisions and geometric motion in Lazare Carnot’s operative mechanics, or Faraday’s experimental science with respect to Ampère’s mechanical approach in the electric current domain, or physico-mathematical choices in Maxwell’s electromagnetic theory. In this paper, we will focus on the historical emergence of mechanical science from a physico-mathematical standpoint and emphasize significant similarities and/or differences in mathematical approaches by some key authors of the 18th century. Attention is paid to the role of mathematical interpretation for physical objects. (shrink)