Scholars have long considered de Philosophia and de Caelo to be in contradiction regarding the nature of the heavenly bodies, particularly with respect to the activity proper to the element composing them. According to the accounts we have of de Philosophia, Aristotle seems to have put forth that stars move because they have minds, and, according to Cicero’s account of the lost text, they choose their actions out of free will. In de Caelo, however, Aristotle seems only to consider that (...) stars engage in the activity of circular motion because it is in their nature to do so, as it is in the nature of, e.g. fire to move upwards or Earth to move downwards. In this paper, I argue against the longstanding view that there is an incompatibility between these two “early” cosmological texts of Aristotle. I aim to show that these two texts endorse complementary, not contradictory, views of the heavenly bodies. I argue that in de Philosophia, Aristotle attributes to stars the intellective counterpart of the spatial motion which is developed in greater depth in de Caelo, while in de Caelo, we see hints of Aristotle’s view in de Philosophia that the stars are also minds and are able to rationally cognize their particular good – a point which is shown in de Caelo 292a18–293a14, where Aristotle attributes both life and praxis to the heavenly bodies. The overarching view which I present of these two texts is that while de Caelo approaches the heavenly bodies qua bodies and de Philosophia approaches them qua minds, they are still examining one and the same substance and that Aristotle has not changed his mind regarding the basic nature of such a substance in the (supposed) interim between writing de Philosophia and de Caelo. Rather, we find echoes of de Caelo in de Philosophia, and echoes of de Philosophia in de Caelo, which speaks to the fact that Aristotle maintains one view of the heavenly bodies which he presents over the course of these two texts. (shrink)

In developing his theory of aether in De Caelo 1, Aristotle argues, in DC 1.4, that one circular motion cannot be contrary to another. In this paper, I discuss how Aristotle can maintain this position and accept the existence of celestial spheres that rotate in contrary directions, as he does in his revision of the Eudoxan theory in Metaphysics 12.8.

_ Source: _Volume 29, Issue 1, pp 9 - 38 Hobbes tried to develop a strict version of the mechanical philosophy, in which all physical phenomena were explained only in terms of bodies in motion, and the only forces allowed were forces of collision or impact. This ambition puts Hobbes into a select group of original thinkers, alongside Galileo, Isaac Beeckman, and Descartes. No other early modern thinkers developed a strict version of the mechanical philosophy. Natural philosophies relying solely (...) on bodies in motion require a concept of inertial motion. Beeckman and Descartes assumed rectilinear motions were rectilinear, but Galileo adopted a theory which has been referred to as circular inertia. Hobbes’s natural philosophy depended to a large extent on what he called “simple circular motions.” In this paper, I argue that Hobbes’s simple circular motions derived from Galileo’s belief in circular inertia. The paper opens with a section outlining Galileo’s concept, the following section shows how Hobbes’s physics depended upon circular motions, which are held to continue indefinitely. A third section shows the difficulty Hobbes had in maintaining a strictly mechanistic philosophy, and the conclusion offers some speculations as to why Galileo’s circular inertia was never entertained as a serious rival to rectilinear inertia, except by Hobbes. (shrink)

An account of Copernicus's doctrine of gravity and of its various sources, among them Stoic, Neoplatonic and scholastic.

In a recent paper in Astrophysics and Space Science Vol. 364 no. 11 (2019), S. Ershkov & D. Leschenko presented a new solving procedure for Euler-Poisson equations for solving momentum equations of the CR3BP near libration points for uniformly rotating planets having inclined orbits in the solar system with respect to the orbit of the Earth. The system of equations of the CR3BP has been explored with regard to the existence of an analytic way of presentation of the approximated solution (...) in the vicinity of libration points. A new and elegant ansatz has been suggested in their publication whereby, in solving, the momentum equation is reduced to a system two coupled Riccati ODEs. In this paper, we presented a numerical solution of such coupled Riccati ODEs using Mathematica software package. (shrink)

This paper explores the Cartesian physics of circular motion, in particular, the long-standing puzzle concerning the possible role of a circular inertial concept in Descartes' theories. Although some commentators have claimed that Descartes' famous "rotating sling" examples favor a rotational component of "striving" towards motion, and that this aspect of his project constitutes a form of inertial thinking, it will be argued that a much stronger case for a Cartesian brand of rotational inertial motion can (...) be constructed from a little-known correspondence, the letter to Ciermans, dated 1638. (shrink)

The Stoic theory of recurrence is founded on Stoic biological and cosmological doctrines. This paper argues that these connections are far more elaborate and well-determined than generally assumed. Evidence from the Stoic theory of the motion of pneuma is brought to bear and a rival geometric model of time is supported against the standard linear and circular models supported by Salles and Long. The new ‘torus model’ is inspired by Alexander of Aphrodisias’ inquisitive questioning of what form the (...) peculiar motion of pneuma may possibly have and based on the evidence in which the Stoics discuss the simultaneous inward/outward motion of pneuma. A new perspective is offered as to what form this motion may take, which ultimately offers an insight into the mechanics of recurrence as also some of the long-standing paradoxes of recurrence. (shrink)

According to Aristotelian physics, there was a fundamental distinction between natural and violent motion. When the cause of the motion was internal to the moving body, that motion was regarded as natural. Violent motion was supposed to have an external efficient cause. It should stop as soon as this external cause ceased its action. The fall of a body was believed to have an internal cause – the very nature of the heavy body – but the (...) motion of a projectile was supposed to be accidental and a violent one, produced by an external agent and maintained by the continuous action of the air around it. Those distinctions disappeared from physics during the 17th century. Descartes and Newton do not address those problems. However, in Galileo’s thought those distinctions were still present, and they did play a relevant role in his physics. Some central arguments presented by Galileo Galilei in the Dialogues concerning the two chief world systems depended on the characterisation of circular motion as “natural”. Considerations concerning natural or violent motion, circular and straight motions, provided a trap that led Galileo astray to ideas that seem extremely odd, from the point of view of classical mechanics. This article shows how Galileo struggled with those Aristotelian concepts when he tried to understand the nature of the motion of falling bodies. (shrink)

Descartes holds that, insofar as nature is a purposeless, unthinking, extended substance, there could be no final causes in physics. Descartes’ derivation of his three laws of motion from the perfections of God thus underwrites a rejection of Aristotle’s conception of natural self-motion and teleology. Aristotle derived his conception of the purposeful action of sublunar creatures from his notion that superlunar bodies are perfect, eternal, living beings, via the thesis that circular motion is more complete or (...) perfect than rectilinear motion. Descartes’ reduction of circular motion to rectilinear motion, achieved through his theological foundation of the laws of motion, thus marks a crucial break from Aristotle’s philosophy of nature. This paper argues that the shift from the Aristotelian conception of nature as self-moving and teleological to the Cartesian conception of nature as purposeless and inert, is not an empirical discovery but is rooted in differing conceptions of where perfection lies in nature. (shrink)

This paper focuses on the mathematisation of mechanics in the seventeenth century, specifically on how the representation of compounded rectilinear motions presented in the ancient Greek Mechanica found its way into Newton’s Principia almost two thousand years later. I aim to show that the path from the former to the latter was optical: the conceptualisation of geometrical lines as paths of reflection created a physical interpretation of dia­grammatic principles of geometrical point-motion, involving the kinematics and dynamics of light reflection. (...) Upon the atomistic conception of light, the optical interpretation of such geometrical principles entailed their mechanical generalisation to local motion; rectilinear motion via the physico-mathemat­ics of reflection and the Mechanica’s parallelogram rule; circular motion via the physico-mathematics of reflection, the Archimedean squaring of the circle and the Mechanica’s extension of the parallelogram rule to centripetal motion. This appeal to the physico-mathematics of reflection forged a realist founda­tion for the mathematisation of motion. Whereas Aristotle’s physics rested on motions which had their source in the nature of the elements, early modern thinkers such as Harriot, Descartes, and Newton based their new principles of mechanical motion upon selected elements of the mechanics of light motion, projected upon the geometry of the parallelogram rule for rectilinear and, ultimately, circular motion. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Extraordinary Rendition:On Politics, Music, and Circular MeaningsRandall Everett AllsupThe purpose of this symposium is to look at music, education, and politics. I will begin with an examination of how musical meanings are politically rendered, and how these understandings are attached to moral consequences. Highly resistant to classification, musical meanings are those things we come to understand about ourselves through music, as opposed to musical knowledge which is demonstrable (...) know-how. While marching bands and flute sonatas can be judged with scores estimated to the 100th decimal point, the meanings that are created between the standards of practice of a given genre and the worldview of the listener or performer are provisional at best. Seen in this light, even seemingly secure or knowable realms like Christian heavy metal or anti-war movies are in fact highly un-objective and unpredictable. (More on Christian rock and movies in a moment). The challenge this paper seeks to uncover is participation on the hither side of fact, where understandings are rendered in a world that is contingent, political, and always in motion. What better example of the unclassifiable than the moving axes of politics and art?So what occurs between art and human or so-called "world" experience? [End Page 144] Let's agree that there is always motion, non-neutral, political movement in this interaction. We need not be students of French post-structuralism to recognize that we are part of many ever-evolving human-made systems, some of control, regulation, reward, punishment, and pleasure, but each with their own gravitation pull.1 I like Susan Sontag's take the best when she wrote that every place, every history has its own "sensibility," its own ineffable way of being in the world.2 Sensibilities—perhaps a clearer way of referring to politics in the context of art and experience—do not exist apart from their environment, yet they are more elusive than an idea or recognizable behavior.3 The sensibility of a time and place makes possible multiple discourses through which we make meaning.4 Some discourses, Foucault would remind us, are intensified by a history's particular sensibility and so appear louder than others. Such a discourse might speak so loudly that it shapes the meanings we make, drowning out options, and thus appearing obvious or commonsensical. The logic of musical assessment and evaluation—scoring marching bands and flute sonatas to the 100th decimal—is one such example.In spite of authoritative voices and reasonable discourses, each history's sensibility has its own escape routes, its own distortions and contradictions. I am fascinated by how we comply with or resist these pulls, as they are matters of agency and identity, matters of equity and social justice. In the present-day context of neo-liberalism and conservative values, especially 21st Century American fundamentalism, we would do well to ask how—not whether—such a fundamentalist sensibility shapes our ways of doing and knowing.5 My attempt is to locate music education in such a project.Shortly after the invasion of Iraq, I wrote a short piece on the fundamentalist imagination and its pull on the arts and education.6 This research took place at the 2003 MENC biennial where Bennett Reimer asks philosophy SRIG participants to consider (among other things) the role of metaphor in music education.7 I viewed the fundamentalist imagination as antithetical to metaphor: to paraphrase, the fundamentalist philosophy of education was "a philosophy for, not with, its initiates. Judgments are passed, not reached; answers are given, not argued... [Most importantly,] it is an educational method that emphasizes and then measures what is literal."8Since then, the voices of American literalism have appeared in increasingly loud volume seeking to discourage interpretation and argument in favor of handed-down teachings and binary logic. Supreme Court Justice Antonin Scalia decries the folly of a "living" constitution, in favor of a strict or literal reading. Retired Cardinal Bernard Law of Boston, in response to a common ground initiative by the late Joseph Bernadin, labels an appeal to "dialogue" a "fundamental flaw."9 Law sniffed, "Dissent from revealed truth or the authoritative [End Page 145] teaching of the church cannot... (shrink)

Here I reexamine Duhem's question of the continuity between medieval dynamics and early modern conservation theories. I concentrate on the heavens. For Aristotle, the motions of the heavens are eternally constant (and thus mathematizable) because an eternally constant divine Reason is their mover. Duhem thought that impetus and conservation theories, by extending sublunar mechanics to the heavens, made a divine renewer of motion redundant. By contrast, I show how Descartes derives his law of conservation by extending Aristotelian celestial dynamics (...) to the earth. Descartes argues that motion is intrinsically linear, not circular. But he agrees that motion is mathematically intelligible only where divine Reason moves bodies in a constant and eternal motion. Descartes strips bodies of active powers, leaving God as the only natural mover; thus both celestial and sublunar motions are constant, and uniformly mathematizable. The law of conservation of the total quantity of motion is an attempt to harmonize the constancy derived a priori with the phenomenal inconstancy of sublunar motions. (shrink)

When Descartes famously claimed that he could explain the world in terms of matter in motion, he was sounding the mantra of seventeenth century science. Though his enthusiasm about this new science has been appreciated and is well documented, the details of his contribution are viewed as riddled with paradox. These purported paradoxes revolve around Descartes's circular definition of 'motion' and 'a body', which seems to render his account of individuation implausible. ;I argue for a new interpretation (...) of the Cartesian ontology under which these purported paradoxes, identified in Descartes's metaphysics by commentators including Kenny, Prendergast, and Garber, simply do not arise. ;In contrast to interpretations of Descartes as committed to many individual extended substances, I argue that Descartes is committed to only one individual extended substance-the whole extended universe. In my interpretation, bodies have a quasi-individual status: they acquire their individuality because the extended universe appears to perceivers as if it were divided into things like pieces of wax, stones, or birds. As quasi-individuals, bodies are also quasi-substances; this means that while they derive their materiality from the whole extended universe, they receive their individuality from human perception. I explain that the substantiality of bodies is tertiary because it involves dependence on the whole extended universe and on minds. Thus, individual bodies differ from God, who has primary substantiality because of his absolute independence, and also from the whole extended universe and minds, both of which have secondary substantiality because they are dependent solely on God. In this way, I argue that Descartes held a kind of phenomenalism about the individuation of bodies . My account is thus similar in spirit to those offered by Martial Gueroult and Thomas Lennon, though it differs sharply from both. ;I also give interpretations of clear and distinct perceptions of the real, conceptual, and modal distinctions of substances on the three levels. I show how bodies become individuated. I conclude by showing why Descartes's circular definition of motion and bodies is virtuous and not vicious. (shrink)

The metaphysical commitment to the circle as the essential element in the analysis of celestial motion has long been recognized as the hallmark of classical astronomy. What has not always been clear, however, is that the circle continued to serve Kepler as a central element in his astronomy after the discovery of the elliptical orbit of Mars. Moreover, the circle also functioned for Kepler in geometry to select the basic polygons, in music to select the basic harmonies, and in (...) astrology to select the basic aspects. His basic set of polygons consisted of those figures that could be constructed using only a compass and a rule; the set of fundamental harmonies consisted of the consonances of the just intonation; and the traditional set of astrological aspects were enlarged by Kepler to include three new aspects in order to make the astrological set consistent with geometry and music. And as the circle served to unify these three areas, so also did it serve to supply the fundamental answers to astronomical problems well after the discovery of his new astronomy—a topic to be discussed in Part II of this paper. (shrink)

The metaphysical commitment to the circle as the essential element in the analysis of celestial motion has long been recognized as the hallmark of classical astronomy. Part I of this paper contains...

Appeal to faith is not uncommon in disputes about the mind-body problem. It is tempting to assume that dualists are more likely than physicalists to presuppose faith in supporting their conclusions, but in recent years physicalists have made claims of faith a standard practice. Of course, their version of faith is peculiar, a faith commitment that my colleague, Brendan Sweetman, has called "the scientific faith argument." This type of reasoning is typified by the remarks of J. J. C. Smart: "...the (...) suggestion I wish to resist is... to say 'I have a yellowish-orange after-image' is to report something irreducibly psychical.... It seems to me that science is increasingly giving us a viewpoint whereby organisms are able to be seen as physico-chemical mechanisms; it seems that even the behavior of man himself will one day be explicable in mechanistic terms". Some physicalists assert their faith stridently and dogmatically. Take Paul M. Churchland, for instance: "The human species and all of its features are the wholly physical outcome of a purely physical process.... If this is the correct account of our origins, then there seems neither need, nor room to fit any nonphysical substances or properties into our theoretical account of ourselves. We are creatures of matter. And we should learn to live with that fact". Of course, these views are mere assertions rather than arguments and they reflect a question-begging procedure. But since naturalism--the view that life and consciousness are nothing but the products of physics, matter in motion--is granted a priori by so many in philosophy today, the petitio principii has become the argument of choice. (shrink)

James A. Diefenbeck, Wayward Reflections on the History ofPhilosophyThomas R. Flynn Sartre, Foucault and Historical Reason. Volume 1:Toward an Existential Theory of HistoryMark Golden and Peter Toohey Inventing Ancient Culture:Historicism, Periodization and the Ancient WorldZenonas Norkus Istorika: Istorinis IvadasEverett Zimmerman The Boundaries of Fiction: History and theEighteenth‐Century British Novel.

Since there is no really elaborated theory of the dialectic of nature, it is not only desirable but necessary to take a look at some of Hegel's original intuitions, which in many cases lost their distinctness in his later works, or fell victim to the exigencies of his system. Philosophy makes use not only of reasoning but also of intuition. In respect of the mass which offers persistent resistance to a notional solution, it is important to find a suitable image (...) for developing a first approximation to the understanding of the question. According to Hegel, the metaphors of circular and gyratory motion are well-suited for this. Here it is essential to clarify what we can gain by a structural interpretation of such ideas. I think that an attempt has to be made to bring out the contemporary relevance of the topic. Doing so is always a delicate matter, but it is a must if undertakings of the present kind are to be anything more than philological expositions of Hegel's philosophy, if they are to make a real contribution to reflection on the foundations of physics. I shall first give a brief review of the arguments put forward in the Encyclopedia; then I shall analyse Hegel's interpretation of circular and gyratory motion and discuss the possibility of bringing out the relevance of his ideas; finally, I shall draw certain conclusions in respect of the principles involved in comprehending the divisibility of matter, and in putting forward a philosophical interpretation of the theory of relativity. (shrink)

According to some currents of modern historiography, Galilei's propensity for circular motion would have led him to consider this and not rectilinear motion as “natural motion”; therefore the principle of inertia could not be fully attributed to Galileo, which he would never have formulated. The question of the authorship of the principle of inertia certainly weighs on both nationalistic elements and returns of antigaleleism, while the question of its not explicit formulation as a principle is due (...) to ignorance of the type of organization that Galileo intended to give to the exposition of his physics. The author, after having hinted at possible prodromes of the principle of inertia and having reported the adverse opinions of illustrious historians of science (A. Koyré, I. B. Cohen, P. M. Duhem, P. Rossi, G. Holton), through a careful analysis of the Galilean writings, conducted on the digital versions with the help of text analysis programs, firmly reaffirms Galileo's authorship of the principle of inertia and the consequent principle of classical relativity. (shrink)

According to some currents of modern historiography, Galilei's propensity for circular motion would have led him to consider this and not rectilinear motion as “natural motion”; therefore the principle of inertia could not be fully attributed to Galileo, which he would never have formulated. The question of the authorship of the principle of inertia certainly weighs on both nationalistic elements and returns of antigaleleism, while the question of its not explicit formulation as a principle is due (...) to ignorance of the type of organization that Galileo intended to give to the exposition of his physics. The author, after having hinted at possible prodromes of the principle of inertia and having reported the adverse opinions of illustrious historians of science (A. Koyré, I. B. Cohen, P. M. Duhem, P. Rossi, G. Holton), through a careful analysis of the Galilean writings, conducted on the digital versions with the help of text analysis programs, firmly reaffirms Galileo's authorship of the principle of inertia and the consequent principle of classical relativity. (shrink)

The nature of light is a focus of Thomas Hobbes’s natural philosophical project. Hobbes’s explanation of the light of lucid bodies differs across his works, from dilation and contraction in Elements of Law to simple circular motions in De corpore. However, Hobbes consistently explains perceived light by positing that bodily resistance generates the phantasm of light. In Letters I.XIX–XX of Philosophical Letters, fellow materialist Margaret Cavendish attacks the Hobbesian understanding of both lux and lumen by claiming that Hobbes has (...) illicitly made abstractions from matter. In this paper, I argue that Cavendish’s criticisms rely on an incorrect understanding of the nature of Hobbesian geometry and the role it plays in Hobbes’s natural philosophy. Rather than understanding geometry as wholly abstract, Hobbes attempts to ground geometry in different ways of considering bodies and their motions. Furthermore, Hobbes’s own criticisms of abstraction suggest that he would share many of the worries she raises but deny that he falls prey to them. (shrink)

ObjectiveThe correlation between the performance of coordination movement and brain activity is still not fully understood. The current study aimed to identify activated brain regions and brain network connectivity changes for several coordinated finger movements with different difficulty levels and to correlate the brain hemodynamics and connectivity with kinematic performance.MethodsTwenty-one right-dominant-handed subjects were recruited and asked to complete circular motions of single and bilateral fingers in the same direction and in opposite directions on a plane. Kinematic data including radius (...) and angular velocity at each task and synchronized blood oxygen concentration data using functional near-infrared spectroscopy were recorded covering six brain regions including the prefrontal cortex, motor cortex, and occipital lobes. A general linear model was used to locate activated brain regions, and changes compared with baseline in blood oxygen concentration were used to evaluate the degree of brain region activation. Small-world properties, clustering coefficients, and efficiency were used to measure information interaction in brain activity during the movement.ResultIt was found that the radius error of the dominant hand was significantly lower than that of the non-dominant hand in both clockwise and counterclockwise movements. The fNIRS results confirmed that the contralateral brain region was activated during single finger movement and the dominant motor area was activated in IP movement, while both motor areas were activated simultaneously in AP movement. The Δhbo were weakly correlated with radius errors. Brain information interaction in IP movement was significantly larger than that from AP movement in the brain network in the right prefrontal cortex. Brain activity in the right motor cortex reduces motor performance, while the right prefrontal cortex region promotes it.ConclusionOur results suggest there was a significant correlation between motion performance and brain activation level, as well as between motion deviation and brain functional connectivity. The findings may provide a basis for further exploration of the operation of complex brain networks. (shrink)

The reconstruction of the teachings of Аnaximander about the origin of the world is based on the analysis of his practical attempts to simulate some natural phenomena and invent devices or scientific instruments that explain and predict some meteorological events. The Earth rests in equilibrium not only because of its location in the center of the Universe, but also because it is «supported» by the «shell» of «ἀήρ». In the formation of the world, due to the eternal circular (...) class='Hi'>motion, from a mixture of hot and cold stood out «ἀήρ» and «αἰθήρ», constituting the contradictory essence of «apeiron». Pairs of opposites: hot and cold; wet and dry – the energy component of the material principle. Due to the eternal irreversible fatal cyclic process of interaction of these pairs of opposites there is a constant renewal in nature. «Apeiron» in accordance with the immanently inherent property of purposive authority of the law of global processes taking place in it, a fatal impersonal force and unavoidable response for its violation, provides a just balance of forces in the Universe as a whole. (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)

This article aims at clarifying some issues raised by a recent book of Daniel W. Graham about the Presocratic cosmology. It particularly intends to shed some light on the understanding of Anaxagoras’ universe by suggesting some reasons why, despite Graham’s opinion, it is still possible to think that the stars were flat according to him. Another goal is highlighting the importance of the comprehensive physical theory of Anaxagoras, based on a circular motion called perichoresis, which would explain diverse (...) phenomena in a consistent way by introducing simplicity in his cosmology. (shrink)

The theory of vortices seems to contradict Descartes’s willingness to accept in physics only “principles also accepted in mathematics.” We show that this cosmological theory is on the contrary consistent with the Cartesian mathematical norm – explaining phenomena only by the properties that bodies have in common with mathematical objects – and partly implied by the thesis according to which the essence of matter consists of extension – circular motion being the only one allowing movement in a world (...) saturated by a homogeneous extension. In this respect, the incoherence of the Principles of Philosophy resides rather in the gap between the claim to have “proved by mathematical demonstration” and in the fact that, to pass from the level of general principles to that of cosmology, Descartes sets up a series of auxiliary hypotheses concerning the genesis of the world. (shrink)

Several theoretical publications on the Dirac equation published during the last decades have shown that, an interpretation is possible, which ascribes the origin of electron spin and magnetic moment to an autonomous circular motion of the point-like charged particle around a fixed centre. In more recent publications an extension of the original so called “Zitterbewegung Interpretation” of quantum mechanics was suggested, in which the spin results from an average of instantaneous spin vectors over a Zitterbewegung period. We argue (...) that, the corresponding autonomous motion of the electron should, if it is real, determine non-relativistic spin measurements. Such a direct connection with the established formal quantum mechanical description of spin measurements, into which spin is introduced as a “non-classical” quantity has, to our knowledge, not been reported. In the present work we show that, under certain “model assumptions” concerning the proposed autonomous motion, results of spin measurements, including measurements of angular correlations in singlet systems, can indeed be correctly described using classical probabilities. The success of the model is evidence for the “reality” of the assumed autonomous motion. The resulting model violates the Bell—inequalities to the same extent as quantum mechanics. (shrink)

In 1454 Georg Peurbach taught astronomy at the Collegium Civium in Vienna by reading a work of his own: the Theoricae novae planetarum. In 1483 Albert of Brudzewo, teaching astronomy at Cracow University, adopted Peurbach’s text together with a commentariolum of his own. Among the numerous commentaries preserved both in manuscript and in printed form, Brudzewo’s stands out because it submits Peurbach’s work to a subtle analysis that, while recognising the merits for which it was widely accepted, also focuses on (...) the limitations of the celestial spheres described in it. Budzewo’s commentary is of interest, in itself both for its criticism of Peurbach’s descriptions of solar, lunar and planetary theory and also for its importance to Copernicus’s own planetary theory. For Copernicus makes clear in the Commentariolus that his concern was the very same issue, violation of uniform circular motion by the rotation of spheres, that Brudzewo criticises in detail. In this way, Brudzewo’s commentary stands as the original motivation for the investigation of the motion of the planets that was eventually to lead Copernicus to a planetary theory based strictly upon uniform rotation of spheres, and through that investigation to the motion of the Earth and the heliocentric theory. (shrink)

By a simple revision of Newton's diagram for Proposition 6 of the third edition of the Principia, one can see directly how the mathematics of uniform circular motion have been employed to solve the Kepler problem of elliptical planetary motion in Proposition 11. Newton strove initially to build his dynamics on the linear kinematics of Galileo; and, in this utilization of uniformly accelerated linear motion to solve more complicated problems, he can be seen as revolutionary. But (...) he could not escape completely from the coils of celestial circularity, and in his utilization of uniform circular motion to solve problems of elliptical motion, he can be seen as reactionary. The key to understanding Newton's mature dynamics resides in the discussion of the alternate dynamics ratio, as presented here in section six. (shrink)

In chapters 12-18 of "Against Proclus," Philoponus continues to do battle against Proclus' arguments for the beginninglessness and everlastingness of the ordered universe. In this final section there are three notable issues under discussion. The first concerns the composition of the heavens and its manner of movement. Philoponus argues against the Aristotelian thesis that there is a fifth heavenly body that has a natural circular motion. He concludes that even though the celestial region is composed of fire and (...) the other three elements, it can move in a circle by the agency of its soul, and that this circular motion is not compromised in any way by the innate natural motion of the fire. Chapter 16 contains an extended discussion of the will of God and His relation to particulars. Here Philoponus addresses issues that become central to medieval philosophical and theological discussions, including the unity, timelessness and indivisibility of God's will. Finally, throughout these seven chapters Philoponus is engaged in a detailed exegesis of Plato's Timaeus which aims to settle a number of familiar interpretive problems, notably how we should properly understand the pre-cosmic state of disorderly motion, and the statement that the visible cosmos is an image of the paradigm. Philoponus' exegetical concerns culminate in chapter 18 with an extensive discussion of Plato's attitude to poetry and myth. (shrink)

Aberrations -- Absorption -- Accuracy and precision -- Alpha radiation -- Amplitude -- Angular forces -- Angular momentum -- Antenna -- Arago dot -- Aperture -- Archimedes's principle -- Band theory of solids -- Bernoulli's principle -- Beta radiation -- Blackbody radiation -- Bohr atom -- Bose condensation -- Bra-ket notation -- British thermal unit (BTU) -- Calculating system efficiency -- Circular motion -- Closed systems and isolated systems -- Concave and convex -- Conservation of charge -- Conservation (...) of energy -- Convection and conduction -- Cosmic radiation -- Crest and trough -- Density and specific gravity -- Diode -- Distance and area -- Distortion -- Doppler effect -- Dynamic systems theory -- Edison effect -- Eigenvectors -- Elastic and inelastic collisions -- Electric circuits: Parallel vs series, diagrams and components -- Electric potential -- Energy and power -- Enthalpy -- Entropy -- Euler's laws of motion -- Falling bodies and physics -- Faraday's law -- Feynman diagrams -- Flywheel -- Focal point -- Free body diagram -- Frequency -- Gamma radiation -- Gauss's law -- Gluon -- Gravitational potential energy -- Harmonic oscillator -- Harmonics -- Heisenberg uncertainty principle -- Higgs boson -- Horsepower -- Ideal gas law -- Joule --. (shrink)

Introduction Conatus is a specific concept within Descartes’s physics. In particular, it assumes a crucial importance in the purely mechanistic description of the nature of light – an issue that Des- cartes considered one of the most crucial challenges, and major achievements, of his natural phil- osophy. According to Descartes’s cosmology, the universe – understood as a material continuum in which there is no vacuum – is composed of a number of separate yet interconnected vortices. Each of these vortices consists (...) in a set of bands rotating around their centres. The bands are com- posed of corpuscles of the three elements, each distinguished on the basis of their different shapes and sizes. The small globules of the second element, although impeded by the other parts of heaven, strive to move away from the centre of the vortex around which they revolve, thus exerting a certain force against the surrounding bodies. This striving or conatus, though a mere force rather than a genuine motion, is transmitted instan- taneously and along straight lines from body to body. According to Descartes, then, the nature of light consists in this striving alone. This account must be understood as strictly connected to the fundamental laws that regulate the Cartesian world. It is particularly important to recall that for Descartes the centrifugal force exerted by a rotating body is understood to be a consequence of the intrinsic rectilinearity of every motion. As the second of the three Laws of Nature set forth in Book II of the Principles of Philosophy establishes, “all motion is in itself rectilinear; and hence any body moving in a circle tends to move away from the centre of the circle which it describes as proved by the fact that a stone rotating in a sling tends to move centrifugally along the tangent of each point described by a circle.1 Similarly, each of the globules of the second element “strives to recede with a great force from the centre of the vortex in which it rotates; it is in fact prevented by the other globules placed all around, not differently than a stone in a sling”. Within this framework, as I show later, conatus occurs when a body’s intrinsic tendency to rectilinear motion is impeded by an external constraint. As Stephen Gaukroger notes, the use of the term conatus in the Principles – like “vis” and “ action ” – shows that Descartes “cannot avoid dynamic terminology”, despite his declared intent “to construe motion in a purely kinematic way”. Indeed, Gaukroger observes that the notions of force action and striving are systematically employed in the Principles – appearing 290, 59 and 8 times, respectively. Also noteworthy, conatus was – together with the more familiar concepts of actio and vis – a significant element of the conceptual apparatus of Scholastic natural philosophy. As will be seen later – and this is the first goal of this paper – here the concept of conatus had a very specific function. Indeed, it was a central part of the Aristotelian- Scholastic account of gravitation. Conatus was used to refer to the striving of a body to move towards its natural place – especially in cases where its natural motion was hindered or impeded by an external mover. This specific use of the concept of conatus can be found in texts on natural philosophy from the end of the sixteenth through the late seventeenth century. Notably, it occurs in some of the late -Scho- lastic texts which held special significance for Descartes’s thought. Therefore, Descartes introduces conatus in a context in which this concept already had a very specific meaning, and one of which he was very probably aware. The possible relations between these two apparently very different con- cepts have therefore to be scrutinized. I thereby propose to undertake a comparison between the Scho- lastic and the Cartesian conceptions of conatus. I hope to show that certain traits of the former are indeed echoed by the latter, although adapted to the much changed physical paradigm of Cartesian physics. In fact, Descartes’s conatus, though sharing some important similarities with the old one, underwent significant transformations in terms of both its meaning and its application. However, I hope to show that these concepts are both used to describe the behaviour of bodies in relation to their intrinsic motive tendency, and in particular when this tendency is impeded or prevented. Such a reconstruction offers two main areas of interest. On an immediate level, it furthers the general efforts of scholars over the past decades to reconstruct the full extent of the relations between Descartes’s thought and Scholastic philosophy. However, there is another significant reason for taking an interest in the ties between the Scholastic and the Cartesian conceptions of conatus. Indeed, the Cartesian conatus must be seen as crucial to a proper understanding of the broader, diverse conceptualization that this idea enjoyed in the thought of many of the most important philosophers of the early modern period, namely Spinoza, Hobbes and Leibniz. In particular, Spinoza, were directly influenced by Descartes in their unique formulations of conatus. Thus a reconstruction of the context in which Descartes formulated his conatus and of its relations to a pre-existing Scholastic conception will enable us to better reconstruct the history of this idea in the early modern period. The paper is structured as follows: in the first part, I provide a thorough review of the Scho- lastic employment of the concept conatus – both its meaning and the extent of its usage. I then show that it occurs in some of the most prominent Cartesian sources. Finally, I shall provide an account of Descartes’s theory of circular motion and conatus with the specific aim of empha- sizing the elements of both continuity and discontinuity that justify the claim that Descartes’s con- ception of conatus is reminiscent of the Scholastic one. (shrink)

Cannon and Jensen assert that data from different national time laboratories give a test of the interaction interpretation of special relativity theory. That interpretation is to be applied, however, to clocks in relative uniform motion, and therefore is not tested by the time-rate effects associated with different terrestrial locations of clocks. Those effects are described by the general theory of relativity, and arise with differences in gravitational potential and state of circular motion of the clocks. An argument (...) by the authors against invariance of entropy clocks, on grounds of neglect of relativity of simultaneity, is also criticized. (shrink)

T. Kuhn’s theory of scientific revolutions has repeatedly been the subject of criticism. It is important to note that Kuhn pays very limited attention to the phenomenon of the scientific revolution itself, comparing the revolution either with a religious conversion or with a gestalt switch. Such comparisons, however, are very superficial. This paper outlines a new understanding of the scientific revolution as a result of the resonance of the intellectual trends of the early modern period. It was the quasi-simultaneous action (...) of various factors that led to revolutionary changes in natural philosophy, which, in turn, gave rise to the actual scientific revolution. In addition, the article shows that the Copernican Revolution cannot be described within the model of scientific revolution developed by T. Kuhn. Ptolemy’s theory was mathematically constructed so that it could not make inaccurate predictions of planetary motion, because – as we are now clear – the function characterizing the trajectory of planetary motion was actually represented as a Fourier series. The Copernican revolution was not a Kuhn-type scientific revolution, nor was it caused by the empirical failures of Ptolemaic astronomy. Events unfolded according to a different scheme. Copernicus set out to carry out the principle of the uniform circular motion of the planets more consistently than had been done in Ptolemy’s theory, at the same time presenting to this theory those requirements of an aesthetic and methodological order, which the cognitively fragmented system of Ptolemy, for all its flexibility, could not satisfy and, by the conditions of its creation, could not satisfy. In addition, the article shows that Copernicus, in constructing his heliocentric theory, was essentially seeking answers to the challenges that Alberti’s artificial perspective and Nicholas of Cusa’s theological speculation posed to the visual experience in the sixteenth century. (shrink)