This paper aims both to tackle the technical issue of deciphering Hobbes’s derivation of the sine law of refraction and to throw some light to the broader issue of Hobbes’s mechanical philosophy. I start by recapitulating the polemics between Hobbes and Descartes concerning Descartes’ optics. I argue that, first, Hobbes’s criticisms do expose certain shortcomings of Descartes’ optics which presupposes a twofold distinction between real motion and inclination to motion, and between motion itself and determination of motion; second, Hobbes’s (...) optical theory presented in Tractatus Opticus I constitutes a more economical alternative, which eliminates the twofold distinction and only admits actual local motion, and Hobbes’s derivation of the sine law presented therein, which I call “the early model” and which was retained in Tractatus Opticus II and First Draught, is mathematically consistent and physically meaningful. These two points give Hobbes’s early optics some theoretical advantage over that of Descartes. However, an issue that has baffled commentators is that, in De Corpore Hobbes’s derivation of the sine law seems to be completely different from that presented in his earlier works, furthermore, it does not make any intuitive sense. I argue that the derivation of the sine law in De Corpore does make sense mathematically if we read it as a simplification of the early model, and Hobbes has already hinted toward it in the last proposition of Tractatus Opticus I. But now the question becomes, why does Hobbes take himself to be entitled to present this simplified, seemingly question-begging form without having presented all the previous results? My conjecture is that the switch from the early model to the late model is symptomatic of Hobbes’s changing views on the relation between physics and mathematics. (shrink)

This article engages the analogy of Palestine/Israel to apartheid South Africa, and probes the political imaginary that contours this discussion while explicating the circumstances of its emergence. Accordingly, it contends that apartheid is not merely a system of institutionalized separation; rather, it organizes the facts and reality of separation(s) within a frame and against a background unity that effectively allows it to be perceived as such. To that end, the article explores four key factors that created background unity in apartheid (...) South Africa: labor relations; political theology; role of language; and geo-political unit(y), and scrutinizes their political and experiential ramifications in Palestine/Israel. (shrink)

Leibniz proposed the ‘Most Determined Path Principle’ in seventeenth century. According to it, ‘ease’ of travel is the end purpose of motion. Using this principle and his calculus method he demonstrated Snell’s Laws of reflection and refraction. This method shows that light follows extremal (local minimum or maximum) time path in going from one point to another, either directly along a straight line path or along a broken line path when it undergoes reflection or refraction at plane or (...) spherical (concave or convex) surfaces. The extremal time path avoided the criticism that Fermat’s least time path was subjected to, by Cartesians who cited examples of reflections at spherical surfaces where light took the path of longest time. Thereby it became the standard method of demonstration of Snell’s Laws. Ptolemy’s theorem is a fundamental theorem in geometry. A special case of it offers a method of finding the minimum sum of the two distances of a point from two given fixed points. We show in this paper that Leibniz’s calculus proof of Snell’s Laws violates Ptolemy’s theorem, whereby Leibniz’s proof becomes invalid. (shrink)

Fermat’s Least Time Principle has a long history. World’s foremost academies of the day championed by their most prestigious philosophers competed for the glory and prestige that went with the solution of the refraction problem of light. The controversy, known as Descartes - Fermat controversy was due to the contradictory views held by Descartes and Fermat regarding the relative speeds of light in different media. Descartes with his mechanical philosophy insisted that every natural phenomenon must be explained by mechanical (...) principles. Fermat on the other hand insisted an end purpose for every motion. For example, least time of travel and not the least distance of travel is the end purpose for motion of light. This implied a thinking nature, which was rejected by Descartes. Surprisingly, with contradictory assumptions regarding the relative speeds of light in different media, both Descartes and Fermat came to the same result that the ratio of sines of angles of incidence and refraction is a constant. Fermat’s result came to be known as the ‘Fermat’s least time principle’. We show in this article that Fermat’s least time principle violates a fundamental theorem in geometry – the Ptolemy’s theorem. That leads to the invalidity of Fermat’s principle. -/- . (shrink)

Perceptual experiences are not immediately responsive to reasons. You see a stick submerged in a glass of water as bent no matter how much you know about light refraction. Due to this isolation from reasons, perception is traditionally considered outside the scope of epistemic evaluability as justified or unjustified. Is perception really as independent from reasons as visual illusions make it out to be? I argue no, drawing on psychological evidence from perceptual learning. The flexibility of perceptual learning is (...) a way of responding to new epistemic reasons. The resulting perceptual experiences are epistemically evaluable as justified or unjustified. (shrink)

Rene Descartes (1596 – 1650) is considered the founder of modern philosophy. Profoundly influenced by the new physics and astronomy of Kepler and Galileo, Descartes was a scientist and mathematician whose most long-lasting contributions in science were the invention of Cartesian coordinates, the application of algebra to geometry, and the discovery of the law of refraction, what we now call Snell’s law.His most important books on philosophy were The discourse on method(1637) and The meditations(1642). Descartes’ writings display an exemplary (...) degree of clarity and an aversion to pedantry. I explore Descartes' break with Aristotle, but also shine a light on the intellectual continuity Descartes had with Aristotle's thought. I also draw attention to some overlooked but interesting possibilities for an experimental test of a dualistic theory of mind. (shrink)

In this work it is shown how absolute simultaneity of spatially distinct events can be established by means of a general criterion based on isotropically propagating signals and how it can be consistently preserved also when operating with Lorentz-like coordinate transformations between moving frames. The specific invariance properties of these transformations of coordinates are discussed, leading to a different interpretation of the physical meaning of the transformed variables with respect to their prevailing interpretation when associated with the Lorentz transformation. On (...) these basis, the emission hypothesis of W. Ritz is then applied to justify the outcomes of the Fizeau experiment, thanks to the introduction of an additional hypothesis regarding the influence of turbulence on the refractive index of the moving fluid. Finally, a test case to investigate the validity of either the Galilean or the Relativistic velocity composition rule is presented. Such test relies on the aberration of the light coming from celestial objects due to the motion of the observer, and on the analysis of the results obtained by applying the two different formulas to process the data of the observed positions, as measured in the moving frame, in order to determine the actual un-aberrated location of the source. (shrink)

Essays from the political website CounterPunch. - Requiem: Dies Non, Not Dies Irae (September 18, 2001) - Mouth Wide Shut (April 8, 2002) - So Long Frank O. Gehry? (April 28, 2002) - Bête Noire (May 22, 2002) - “All politics is local?”: The Unbearable Lightness of NGOs (May 24, 2002) - Bush and Mies van der Rohe: Architecture and Ideology (June 1, 2002) - The Adventures of Mademoiselle M.: Or Getting Screwed in Paris (June 8-9, 2002) - Loose Lips: (...) Liberty, Democracy and Bush (July 6, 2002) - Go Tell Karl Rove!: The Anti-Republican Party (July 13, 2002) - Be Still My Beating Heart (July 15, 2002) - Grave New Urbanism: The World Trade Center Burlesque (July 20, 2002) - Roamin’ in the Gloamin’: Van Morrison: In September (July 25, 2002) - Sublime Žižek: Guarding Lenin’s Tomb (July 27, 2002) - Vox Populi: Everyone’s a Critic (August 3, 2002) - Auteur-Driven Vehicles: The New New Laocoon (August 19, 2002) - Beaux Rêves, Citoyens!!! (September 5, 2002) - Immortality: The Quest for Fire (August 31, 2002) Parting Shots: A Refracted History (Summary) Of The Twentieth Century (November 2, 2002) - New Books Christmas 2002: Livres Deluxe (December 23, 2002) - The Drunken Flower (July 26, 2003) - The Infernal Machine: “Architectures” in Service to Nothing (August 23, 2003). (shrink)

Theologians often reflect on the ethical uses and impacts of artificial intelligence, but when it comes to artificial intelligence techniques themselves, some have questioned whether much exists to discuss in the first place. If the significance of computational operations is attributed rather than intrinsic, what are we to say about them? Ancient thinkers—namely Augustine of Hippo (lived 354–430)—break the impasse, enabling us to draw forth the moral and metaphysical significance of current developments like the “deep neural networks” that are responsible (...) for some of the most remarkable achievements of the past few years. First, Augustine’s theology of the natural world’s rationes seminales makes sense of neural networks’ success by explaining the world as a kaleidoscopic refraction of divine Wisdom rather than as a collection of discrete objects standing in crisp relations. Second, his account of interpretive judgment as a moral act bound up with love reveals how our training and use of AI relates to the Christian’s assimilation to Wisdom. The contingent meaning of the neural network reveals AI’s potential either for standing between us and the world or in some sense facilitating a Christian’s regathering of the created echoes of divine Wisdom throughout his or her journey into the Trinity. (shrink)

ENG: The essence of the problem of transcendental subject in Kant’s philosophy is considered. The special place of this subject in Kant’s transcendental critical project is defined. The author takes into account not only Kant’s theoretical philosophy, within frame of which the transcendental subject has been first stated, but also practical philosophy, in which the potential and purpose of this subject most completely fulfil. The concept of the transcendental subject is not identical to the subject of thinking, as well as (...) it is not a vestige of pre-Kantian metaphysics. The concept of the transcendental subject is complicated refraction of different representations from rational psychology, metaphysics of substance and critical project in itself. // RUS: Выявляется сущность проблемы трансцендентального субъекта в философии И. Канта. Показывается особое место понятия трансцендентального субъекта в трансцендентально-критическом проекте немецкого мыслителя. При этом во внимание принимается не только теоретическая философия И. Канта, где впервые был заявлен трансцендентальный субъект, но и практическая философия, в рамках которой наиболее полно раскрывается потенциал и предназначение этого субъекта, далеко не тождественного субъекту мышления, но и не являющегося просто рудиментом докантовской метафизики. Содержание понятия трансцендентального субъекта оказывается сложным преломлением различных представлений из рациональной психологии, метафизики субстанции и собственно критического проекта. (shrink)

I propose to take a more proximate and micro-contextual approach to the history of cultural psychology, by focusing on the 1960s. In this historical snapshot, Jerome Bruner emerges as a consummate experimental scientist, organizer of scientific knowledge, and entrepreneur in education. Looking ahead, his work continued to evolve: from perceptual readiness and values in perception (1950s) to thinking and educational psychology (1960s). Then came developmental psychology and spiral curriculum (1970s), language as social interaction (1980s), the narrative turn to meaning (1990s), (...) and legal psychology (2000s). His scientific biography resembles a prism, refracting myriad persons and cultures in which he moved. Within that context it is possible to trace several pathways to cultural psychology. (shrink)

In recent decades, Vygotsky’s sociocultural theory (VST) has become particularly influential in the fields of education and educational psychology. Perezhivanie is an important concept in VST that stipulates a relative influence of environment on a person’s psychological development depending on their age or stage of development. However, perezhivanie has been differentially interpreted and applied in previous literature to suit the purposes of domain-specific research. The lack of a comprehensive theoretical understanding of the concept can undermine research findings and their implications (...) for educational practices. Drawing on a content analysis of Vygotsky’s key texts on perezhivanie, this paper provides a much-needed theoretical discussion that unpacks comprehensively the theoretical content of perezhivanie and the methodological principles guiding its application. The findings revealed that conceptually, perezhivanie can be defined as: (a) a theoretical relation between an individual and their environment, (b) an abstract experience of or attitude towards a life situation and (c) a concrete lived experience of an event within that situation. Four major discernible components of an individual’s perezhivanie include the environmental factor, personal characteristics mobilised, refraction prism and psychological influences. Five key methodological principles were conceived to assist the employment of perezhivanie in educational/psychological research: (1) utilising a perezhivanie as a unit of analysis, (2) analysing perezhivanie at different levels, (3) accounting for the perspective of the individual involved, (4) constructing the refraction prism and (5) determining the major personal characteristics mobilised in the perezhivanie. Implications for educational and research practices are then discussed. (shrink)

In Postpolitics and the Limits of Nature, Andy Scerri offers a comprehensive overview of the relationship between Critical Theory and the US environmental movement from the 1960s to the present, refracted through the lens of the American Left. He examines why past generations of radical ecological and social justice scholarship have been ineffective in the fight against injustice and rampant environmental exploitation. Scerri then engages a new wave of radicals and reformists who, in the wake of the Occupy movement and (...) the 2016 presidential election, are reinventing the radical project as a challenge to injustice in the Anthropocene era. Along the way, he provides a fresh account of the thought of one of the major contributors to critical theory, Theodor Adorno, and of recent work that seeks to link Adorno’s ideas to the so-called new realism in political philosophy and political theory. (shrink)

Throughout his work, Deleuze not only draws on literature in order to address philosophical problems but he seeks to map out the ‘mobile relations’ between philosophy and literature. After an initial overview, I will focus on A Thousand Plateaus (1980), a book co-authored with Guattari, and in particular, on plateaus “1874: Three Novellas or ‘What happened?’” and “1730: Becoming-intense, becoming-animal, becoming-imperceptible…” In doing so, I aim to explore: (a) how the relation between literature and philosophy is refracted in Novellas Plateau (...) and (b) the way in which Deleuze and Guattari articulate their key philosophical notion of becoming-imperceptible via Kierkegaard’s knight of faith. The novella as a literary genre by essentially relating to secrecy also advances a distinctive way of relation between the three dimensions of time (the past, present and future). I argue that novella-time could be extended beyond the limits of the literary genre ‘novella.’ To this end, I propose a reading of Kierkegaard’s Repetition (1843) and selected entries from his Journals in order to identify his contribution as a religious writer to the discussion of philosophy as literature. I conclude that time, change and faith stand out as a common problematic of philosophy, literature, and life. (shrink)

During 17th century a scientific controversy existed on the derivation of Snell’s laws of reflection and refraction. Descartes gave a derivation of the laws, independent of the minimality of travel time of a ray of light between two given points. Fermat and Leibniz gave a derivation of the laws, based on the minimality of travel time of a ray of light between two given points. Leibniz’s calculus method became the standard method of derivation of the two laws. We demonstrate (...) in this article that Snell’s law of reflection follows from simple results of geometry. We do not use the concept of motion or the time of travel in our demonstration. That is, time plays no role in our demonstration. (shrink)

According to a tradition that we hold variously today, the relational person lives most personally in affective and cognitive empathy, whereby we enter subjective communion with another person. Near future social AIs, including social robots, will give us this experience without possessing any subjectivity of their own. They will also be consumer products, designed to be subservient instruments of their users’ satisfaction. This would seem inevitable. Yet we cannot live as personal when caught between instrumentalizing apparent persons (slaveholding) or numbly (...) dismissing the apparent personalities of our instruments (mild sociopathy). This paper analyzes and proposes a step toward ameliorating this dilemma by way of the thought of a 5th century North African philosopher and theologian, Augustine of Hippo, who is among those essential in giving us our understanding of relational persons. Augustine’s semiotics, deeply intertwined with our affective life, suggest that, if we are to own persuasive social robots humanely, we must join our instinctive experience of empathy for them to an empathic acknowledgment of the real unknown relational persons whose emails, text messages, books, and bodily movements will have provided the training data for the behavior of near-future social AIs. So doing, we may see simulation as simulation (albeit persuasive), while expanding our empathy to include those whose refracted behavioral moments are the seedbed of this simulation. If we naïvely stop at the social robot as the ultimate object of our cognitive and affective empathy, we will suborn the sign to ourselves, undermining rather than sustaining a culture that prizes empathy and abhors the instrumentalization of persons. (shrink)

In Against the Day, Pynchon is obsessed with twoness, double worlds, as well as dual realities, and like Deleuze’s concept of repetition, these duplications and twinships are not merely repetition of the same, rather they allow for creativity, reinvention, and becoming. Pynchon’s duplication of fictional and spectral characters intends to critique the notion of identity as does Deleuzian concept of repetition. Not attached to the representational concept of identity as the recurrence of the same, Pynchon’s duplications decenter the transcendental concept (...) in favor of a perpetual becoming and reproduces difference and singularity. Like Deleuze, Pynchon eschews an identity that is always guaranteed, and shows that the repetition of an object or a subject is not the recurrence of the original self-identical object or person. Moreover, Iceland spar, the mystifying calcite, with its doubling effect provides the reader with a view of a world beyond the ordinary, actual world, which is quite similar to what Pynchon’s novel does per se. (shrink)

Effects associated in quantum mechanics with a divisible probability wave are explained as physically real consequences of the equal but opposite reaction of the apparatus as a particle is measured. Taking as illustration a Mach-Zehnder interferometer operating by refraction, it is shown that this reaction must comprise a fluctuation in the reradiation field of complementary effect to the changes occurring in the photon as it is projected into one or other path. The evolution of this fluctuation through the experiment (...) will explain the alternative states of the particle discerned in self interference, while the maintenance of equilibrium in the face of such fluctuations becomes the source of the Born probabilities. In this scheme, the probability wave is a mathematical artifact, epistemic rather than ontic, and akin in this respect to the simplifying constructions of geometrical optics. (shrink)