Historians of seventeenth-century science have frequently asserted that Kepler's laws of planetary motion were largely ignored between the time of their first publication and the publication of Newton's Principia . In fact, however, they were more widely known and accepted than has been generally recognized.Kepler's ideas were, indeed, rather slow in establishing themselves, and until about 1630 there are few references to them in the literature of the time. But from then onwards, interest in them increased fairly rapidly. In (...) particular, the principle of elliptical orbits had been accepted by most of the leading astronomers in France before 1645 and in England by about 1655. It also received quite strong support in Holland.The second law had a more chequered history. It was enunciated in its exact form by a few writers and was used in practice by some others without being explicitly formulated, but the majority, especially after 1645, preferred one or another of several variant forms which were easier to use but only approximately correct. The third law attracted less interest than the others, chiefly perhaps because it had no satisfactory theoretical basis, but it was correctly stated by at least six writers during the period under review.Between about 1630 and 1650 Kepler's Epitome Astronomiae Copernicanae was probably the most widely read work on theoretical astronomy in northern and western Europe, while his Rudolphine Tables, which were based upon the first two laws, were regarded by the majority of astronomers as the most accurate planetary tables available.Kepler's work certainly did not receive all the recognition it deserved, but the extent to which it was neglected has been much exaggerated. (shrink)

In this article, we aim at presenting a thorough and comprehensive explanation of the mathematical and theoretical relation between all the aspects of Ptolemaic planetary models and their counterparts which are built according to Kepler’s first two laws. Our article also analyzes the predictive differences which arise from comparing Ptolemaic and these ideal Keplerian models, making clear distinctions between those differences which must be attributed to the structural variations between the models, and those which are due to the (...) specific parameters Ptolemy determined in the Almagest. We expect that our work will be a contribution for a better understanding not only of the Ptolemaic theories for planetary longitudes through a clearer perception of the way in which Keplerian features are present—or absent—in Ptolemy’s models, but also for a more balanced judgement of different aspects of the contribution of the first two laws of Kepler to the modern astronomical revolution. (shrink)

Kant's views on the epistemological status of physical science provide an important example of how a philosophical system can be applied to understand the foundation of scientific theories. Michael Friedman has made considerable progress towards elucidating Kant's philosophy of science; in particular, he has argued that Kant viewed Newton's law of universal gravitation as necessary for the possibility of experiencing what Kant called true motion, which is more than the mere relative motion of appearances but is different from Newton's concept (...) of absolute motion. In this context, Friedman has provided an account of how Kant must have viewed Newton's supposed derivation of universal gravitation from Kepler's laws, based on, among other things, Kant's claim that Newton really needed to make extra assumptions in order to derive universal gravitation. In this paper, I argue that Friedman's account is incomplete for three reasons. First, Friedman has overlooked an important aspect of how Newton's third law is applied in the relevant sections of the Principia; as a result, Friedman's account partially misconstrues the relation between the planetary phenomena and the theory of universal gravitation. Second, his account fails to account for Kant's apparent belief that Kepler's laws are only empirically-based rules, even though they seem to be necessary for the derivation of universal gravitation and hence also necessary for Kant's own definition of true motion. Third, Friedman has overlooked some remarks by Kant that indicate that Kant thought the crucial properties of universal gravitation could be known without reference to the empirically determined motions of the planets and hence seemingly without any help from Newton. (shrink)

The book you hold in your hands is the outcome of the "ISCS 2013: Interdisciplinary Symposium on Complex Systems" held at the historical capital of Bohemia as a continuation of our series of symposia in the science of complex systems. Prague, one of the most beautiful European cities, has its own beautiful genius loci. Here, a great number of important discoveries were made and many important scientists spent fruitful and creative years to leave unforgettable traces. The perhaps most significant period (...) was the time of Rudolf II who was a great supporter of the art and the science and attracted a great number of prominent minds to Prague. This trend would continue. Tycho Brahe, Niels Henrik Abel, Johannes Kepler, Bernard Bolzano, August Cauchy Christian Doppler, Ernst Mach, Albert Einstein and many others followed developing fundamental mathematical and physical theories or expanding them. Thus in the beginning of the 17th century, Kepler formulated here the first two of his three laws of planetary motion on the basis of Tycho Brahe’s observations. In the 19th century, nowhere differentiable continuous functions (of a fractal character) were constructed here by Bolzano along with a treatise on infinite sets, titled “Paradoxes of Infinity” (1851). Weierstrass would later publish a similar function in 1872. In 1842, Doppler as a professor of mathematics at the Technical University of Prague here first lectured about a physical effect to bear his name later. And the epoch-making physicist Albert Einstein – while being a chaired professor of theoretical physics at the German University of Prague – arrived at the decisive steps of his later finished theory of general relativity during the years 1911–1912. In Prague, also many famous philosophers and writers accomplished their works; for instance, playwright arel ape coined the word "robot" in Prague (“robot” comes from the Czech word “robota” which means “forced labor”). (shrink)

SummaryThis 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. (shrink)

We will examine Kepler's use of a relation between velocity and distance from a centre of circular motion. This relation plays an essential role, through a derivation in chapter 40 of the Astronomia Nova, in the presentation of the Area Law of planetary motion. Kepler transcends ancient and contemporary applications of the distance-velocity relation by connecting it with his metaphysical commitment to the causal role of the Sun. His second main innovation is to replace the astronomical models of his predecessors (...) with an account that derives trajectories from physical principles. In this paper we restrict our attention primarily to the first 40 chapters of Kepler's Astronomia Nova. Hence, we do not discuss Kepler's discovery of elliptical planetary orbits. (shrink)

Epitome V (1621), and consisted of matching an element of area to an element of time, where each was mathematically determined. His treatment of the area depended solely on the geometry of Euclid's Elements, involving only straight-line and circle propositions – so we have to account for his deliberate avoidance of the sophisticated conic-geometry associated with Apollonius. We show also how his proof could have been made watertight according to modern standards, using methods that lay entirely within his power. The (...) greatest innovation, however, occurred in Kepler's fresh formulation of the measure of time. We trace this concept in relation to early astronomy and conclude that Kepler's treatment unexpectedly entailed the assumption that time varied nonuniformly; meanwhile, a geometrical measure provided the independent variable. Even more surprisingly, this approach turns out to be entirely sound when assessed in present-day terms. Kepler himself attributed the cause of the motion of a single planet around the Sun to a set of `physical' suppositions which represented his religious as well as his Copernican convictions; and we have pared to a minimum – down to four – the number he actually required to achieve this. In the Appendix we use modern mathematics to emphasize the simplicity, both geometrical and kinematical, that objectively characterizes the Sun-focused ellipse as an orbit. Meanwhile we highlight the subjective simplicity of Kepler's own techniques (most of them extremely traditional, some newly created). These two approaches complement each other to account for his success. (shrink)

Johannes Kepler dedicated much of his work to discover a law for the refraction of light. Unfortunately, he formulated an incorrect law. Nevertheless, it was useful for anticipating the behavior of light in some specific conditions. Some believe that Kepler did not have the elements to formulate the law that was later accepted by the scientific community, that is, the Snell–Descartes law. However, in this paper, we propose a model that agrees with Kepler’s heuristics and that is also successful (...) in anticipating the behavior of light when it passes through a surface that separates two media with different optical densities. This model adopts strategies that were recommended by Kepler in two types of analogies. The obstacles that led to the failure of the two types of analogies are presented in the article, and we argue that the model proposed here could overcome these specific obstacles. Finally, we show how the proposed model could be articulated with Kepler’s metaphysics of light. (shrink)

This study of the concept of orbit is intended to throw light on the nature of revolutionary concepts in science. We observe that Kepler transformed theoretical astronomy that was understood in terms of orbs [Latin: orbes] and models , by introducing a single term, orbit [Latin: orbita], that is, the path of a planet in space resulting from the action of physical causes expressed in laws of nature. To demonstrate the claim that orbit is a revolutionary concept we pursue (...) three lines of argument. First we trace the origin of the term; second, we document its development and specify the meaning of the novel term as it was introduced into astronomy by Kepler in his Astronomia nova . Finally, in order to establish in what sense the concept is revolutionary, we pay attention to the enduring impact that the concept has had on the relevant sciences, in this case astronomy and indeed physics. We claim that orbit is an instance of a revolutionary concept whose provenance and use can provide the insights we are seeking. (shrink)

: This study of the concept of orbit is intended to throw light on the nature of revolutionary concepts in science. We observe that Kepler transformed theoretical astronomy that was understood in terms of orbs [Latin: orbes] (spherical shells to which the planets were attached) and models (called hypotheses at the time), by introducing a single term, orbit [Latin: orbita], that is, the path of a planet in space resulting from the action of physical causes expressed in laws of (...) nature. To demonstrate the claim that orbit is a revolutionary concept we pursue three lines of argument. First we trace the origin of the term; second, we document its development and specify the meaning of the novel term as it was introduced into astronomy by Kepler in his Astronomia nova (1609). Finally, in order to establish in what sense the concept is revolutionary, we pay attention to the enduring impact that the concept has had on the relevant sciences, in this case astronomy and indeed physics. We claim that orbit is an instance of a revolutionary concept whose provenance and use can provide the insights we are seeking. (shrink)

In his first major publication, the Mysterium Cosmographicum, Johann Kepler undertook to answer several questions--most notably why there are six planets and why their orbits have a particular relative spacing. Neither Kepler's answers to these questions nor the questions themselves survived the transition to Newtonian physics. Kepler's conviction about the importance of his questions, and his early answers to them, provided the foundation for his subsequent scientific work, including the discovery of the laws of planetary motion for which he (...) is now chiefly remembered. Near the end of his career, in 1621, Kepler produced a second edition of the Mysterium, differing from the first only in the addition of copious notes; in it he refers to his Harmonice Mundi as a vindication of the insights of the Mysterium. J. V. Field's new book systematically examines the mathematical cosmology presented in these three volumes. (shrink)

Human rights discourse has been likened to a global lingua franca, and in more ways than one, the analogy seems apt. Human rights discourse is a language that is used by all yet belongs uniquely to no particular place. It crosses not only the borders between nation-states, but also the divide between national law and international law: it appears in national constitutions and international treaties alike. But is it possible to conceive of human rights as a global language or lingua (...) franca not just in a figurative or metaphorical sense, but in a literal or linguistic sense as a legal dialect defined by distinctive patterns of word choice and usage? Does there exist a global language of human rights that transcends not only national borders, but also the divide between domestic and international law? Empirical analysis suggests that the answer is yes, but this global language comes in at least two variants or dialects. New techniques for performing automated content analysis enable us to analyze the bulk of all national constitutions over the last two centuries, together with the world’s leading regional and international human rights instruments, for patterns of linguistic similarity and to evaluate how much language, if any, they share in common. Specifically, we employ a technique known as topic modeling that disassembles texts into recurring verbal patterns. The results highlight the existence of two species or dialects of rights talk—the universalist dialect and the positive-rights dialect—both of which are global in reach and rising in popularity. The universalist dialect is generic in content and draws heavily on the type of language found in international and regional human rights instruments. It appears in particularly large doses in the constitutions of transitional states, developing states, and states that have been heavily exposed to the influence of the international community. The positive-rights dialect, by contrast, is characterized by its substantive emphasis on positive rights of a social or economic variety, and by its prevalence in lengthier constitutions and constitutions from outside the common law world, especially those of the Spanish-speaking world. Both dialects of rights talk are truly transnational, in the sense that they appear simultaneously in national, regional, and international legal instruments and transcend the distinction between domestic and international law. Their existence attests to the blurring of the boundary between constitutional law and international law. (shrink)

This is a short paper covering my own views on the methods and reasons behind the teaching of medical ethics. All the whys and wherefores are discussed and some conclusions reached. This paper is given from a junior doctor's viewpoint but could equally apply to many others.

This is a first attempt at consolidating and extending the lists of biographies of historians of science compiled by George Sarton, Aldo Mieli and François Russo. In doing so, a systematic examination has been made of the Dictionary of scientific biography, and of the relevant parts of the Isis cumulative bibliography and Kenneth May's Bibliography and research manual of the history of mathematics. Material for a supplement is being collected. Readers are invited to send additional material along with their comments.

This article deals with the housing framework of laws, that is, constitutions. It distinguishes between constitution referring to the de jure, formal, written book of laws and codes that assume supreme authority within any structure, and constitution which defines a body of informal, conditional rules and laws that do not have supreme authority but are abided by, owing to various objective, subjective factors. Constitution reflects the gap between aspiration and actuality, and constitution attracts a higher degree of (...) compliance and implementation. Studies have indeed found a negative relationship between formal rights protection and actual rights observance. The article reveals that rights guarantees are more prone to failure than success as they depend substantially on environmental and institutional conditions. This article emphasizes a symbiosis between judicialization and constitutionalization while a policy question needs to be judicial in nature if the judiciary has to decide on it. (shrink)

In France, John Baptist Say has the merit of producing a very superior work on the subject of Political Economy. His arrangement is luminous, ideas clear, style perspicuous, and the whole subject brought within half the volume of [Adam] Smith's work. Add to this considerable advances in correctness and extension of principles.

In the following Kepler suggests a number of different readings of Carroll’s Alice books that would be useful to those attempting to integrate philosophy into an existing curriculum.

Ocherk 1. Voprosy ontologii -- Ocherk 2. Voprosy ėtiki i ėstetiki -- Ocherk 3. Voprosy gnoseologii i aksiologii.

Medical ethics involve more than a prohibition against advertising or solicitation of patients, or a limit on the height of the letters on a doctor's office door. The true ethics of health care are the fundamental values that guide-or should guide-physicians in every aspect of their interaction with patients, their families, and society at large. Professional ethics is a complex and controversial issue, but one that must be dealt with in an era of increasing skepticism about the practice of medicine. (...) Medical Stewardship is a carefully reasoned historical and philosophical inquiry into the origins of our notions of medical ethics, and the ways in which a true sense of the doctor's proper role can be restored. Tracing the development of medical ethics from ancient times to the modern era, Dr. Kepler consides them in relation to the medical profession of today. He considers several areas seldom discussed in works on medical ethics: the exploitation of the patient, preventive versus disease treatment, ethical problems in medical education, drug abuse by physicians, the ethics of organized medicine, and some important but under-utilized roles of the physician. (shrink)

The integration of digital phenotyping in psychiatry promises unprecedented insights into mental health, particularly in college settings where mental well-being is a growing concern. The COVID-19...

Many computational tools for the simulation and design of emergency evacuation and egress are now available. However, due to the scarcity of human and social behavioral data, these computational tools rely on assumptions that have been found inconsistent or unrealistic. This paper presents a multi-agent based framework for simulating human and social behavior during emergency evacuation. A prototype system has been developed, which is able to demonstrate some emergent behaviors, such as competitive, queuing, and herding behaviors. For illustration, an example (...) application of the system for safe egress design is provided. (shrink)

Despite Kepler's candid and detailed report on the discovery of his first two laws, the problem of the origin of these laws still remains unresolved. Attempts to unravel the problem have varied from considering the discovery a chance to one arising from a well-reasoned, patient, and systematic empirical study of Tycho Brahe's observations . On the issue of the influence of non-scientific factors on this discovery also various views exist. Small and Dreyer do not even consider this question. (...) Strong and, to some extent, Westman deny any positive role to such an influence, whereas Koestler and, in some sense, Burtt seem to go to the other extreme. Between these two extremes lie the views of Aiton, Gingerich, Holton, Koyre, and Wilson. I argue that all these attempts are either inaccurate or incomplete because they fail to pay attention to all the relevant factors involved. In Kepler's works and thought I see an interaction among empirical, philosophical, and religious ideas. I show that this interaction had a decisive role to play in the discovery of the laws. If Kepler had emphasized only the empirical, he probably would have been another Tycho, but not the discoverer of the laws and the father of modern astronomy. On the other hand, if he had concentrated only on the philosophical, he would have remained just one among the renaissance natural philosophers. Religious ideas alone also would not have led him to the laws. But when all the three were allowed to interact and collaborate, mutually modifying and complementing each other, the result was the laws. My study has two parts. In the first part I identify and discuss Kepler's religious, philosophical, and scientific ideas. In the second part I discuss his actual discovery of the first two laws. I divide the process of discovery into different stages and show that in each all the three factors had to collaborate to make the discovery possible. I base my studies on Kepler's own original books and letters, supplemented by reflection and commentaries on them by eminent Kepler scholars. (shrink)

This chapter contains section titled: Kepler's New Astronomy Kepler's New Science of Vision Galileo and the Telescope Galileo and the Creation of Mathematical Physics Mersenne and the New Science.