Spin and Wind Directions II: A Bell State Quantum Model

In the first half of this two-part article (Aerts et al. in Found Sci. doi: 10.1007/s10699-017-9528-9, 2017b), we analyzed a cognitive psychology experiment where participants were asked to select pairs of directions that they considered to be the best example of Two Different Wind Directions, and showed that the data violate the CHSH version of Bell’s inequality, with same magnitude as in typical Bell-test experiments in physics. In this second part, we complete our analysis by presenting a symmetrized version of the experiment, still violating the CHSH inequality but now also obeying the marginal law, for which we provide a full quantum modeling in Hilbert space, using a singlet state and suitably chosen product measurements. We also address some of the criticisms that have been recently directed at experiments of this kind, according to which they would not highlight the presence of genuine forms of entanglement. We explain that these criticisms are based on a view of entanglement that is too restrictive, thus unable to capture all possible ways physical and conceptual entities can connect and form systems behaving as a whole. We also provide an example of a mechanical model showing that the violations of the marginal law and Bell inequalities are generally to be associated with different mechanisms.     

Bolzano’s Infinite Quantities

In his Foundations of a General Theory of Manifolds, Georg Cantor praised Bernard Bolzano as a clear defender of actual infinity who had the courage to work with infinite numbers. At the same time, he sharply criticized the way Bolzano dealt with them. Cantor’s concept was based on the existence of a one-to-one correspondence, while Bolzano insisted on Euclid’s Axiom of the whole being greater than a part. Cantor’s set theory has eventually prevailed, and became a formal basis of contemporary mathematics, while Bolzano’s approach is generally considered a step in the wrong direction. In the present paper, we demonstrate that a fragment of Bolzano’s theory of infinite quantities retaining the part-whole principle can be extended to a consistent mathematical structure. It can be interpreted in several possible ways. We obtain either a linearly ordered ring of finite and infinitely great quantities, or a partially ordered ring containing infinitely small, finite and infinitely great quantities. These structures can be used as a basis of the infinitesimal calculus similarly as in non-standard analysis, whether in its full version employing ultrafilters due to Abraham Robinson, or in the recent “cheap version” avoiding ultrafilters due to Terence Tao.     

Theoretical and Conceptual Analysis of the Celebrated 4<Emphasis Type="Italic">π</Emphasis>-Symmetry Neutron Interferometry Experiments

In 1975, two experimental groups have independently observed the \(4\pi \)-symmetry of neutrons’ spin, when passing through a static magnetic field, using a three-blade interferometer made from a single perfect Si-crystal (analogous to the Mach Zehnder interferometer of light optics). In this article, we provide a complete analysis of the experiment, both from a theoretical and conceptual point of view. Firstly, we solve the Schrödinger equation in the weak potential approximation, to obtain the amplitude of the refracted and forward refracted beams, produced by the passage of neutrons through one of the three plates of the LLL interferometer. Secondly, we analyze their passage through a static magnetic field region. This allows us to find explicit expressions for the intensities of the four beams exiting the interferometer, two of which will be interfering and show a typical \(4\pi \)-symmetry, when the strength of the magnetic field is varied. In the last part of the article, we provide a conceptual analysis of the experiment, showing that a neutron’s phase change, when passing through the magnetic field, is due to a longitudinal Stern–Gerlach effect, and not to a Larmor precession. We also emphasize that these experiments do not prove the observability of the sign change of the wave function, when a neutron is \(2\pi \) rotated, but strongly indicate that the latter, like any other elementary “particle,” would be a genuinely non-spatial entity.     

Why Should We Be Pessimistic About Antirealists and Pessimists?

The pessimistic induction over scientific theories (Poincaré in Science and hypothesis, Dover, New York, 1905/1952) holds that present theories will be overthrown as were past theories. The pessimistic induction over scientists (Stanford in Exceeding our grasp: science, history, and the problem of unconceived alternatives, Oxford University Press, Oxford, 2006) holds that present scientists cannot conceive of future theories just as past scientists could not conceive of present theories. The pessimistic induction over realists (Wray in Synthese 190(18):4321–4330, 2013) holds that present realists are wrong about present theories just as past realists were wrong about past theories. The pessimistic induction over antirealist theories (Park in Organon F 21(1):3–21, 2014) holds that the latest antirealist explanation of the success of science (Lyons in Philos Sci 70(5):891–901, 2003) has hidden problems just as its eight predecessors did. In this paper, I (1) criticize the pessimistic inductions over scientific theories, scientists, and realists, (2) introduce a pessimistic induction over antirealist theories, and then (3) construct two new pessimistic inductions. One is a pessimistic induction over antirealists according to which the author of the latest antirealist proposal cannot see hidden problems with his proposal just as his antirealist predecessors could not see hidden problems with their proposals. The other is the pessimistic induction over pessimists according to which since past pessimists have been wrong about their present scientific theories from the early twentieth century to the early twenty-first century, future pessimists will also be wrong about their present scientific theories from the early twenty-first century to the early twenty-second century.     

The Infinite Turn and Speculative Explanations in Cosmology

Infinity, in various guises, has been invoked recently in order to ‘explain’ a number of important questions regarding observable phenomena in science, and in particular in cosmology. Such explanations are by their nature speculative. Here we introduce the notions of relative infinity, closure, and economy of explanation and ask: to what extent explanations involving relative or real constructed infinities can be treated as reasonable?     

Approximation,Mad Men and the Death of JFK

In this article I take the US television series Mad Men (2007—present) as an exemplary ‘approximation’, a term I adopt to signal the way in which certain texts construct a changeable, fluid ‘truth’ resulting from collisions, exchange and dialectical argument. Approximations are layered, their formal layerings mirroring a layered, multifaceted argument. Mad Men integrates and represents real historical events within a fictional setting, and act that suggests that an event or action can never be finished, fixed and not open to reassessment. Specifically, this article examines ‘The Grown Ups’, Episode 12 of Season 3, which charts the events of 22 November 1963, the day Kennedy was assassinated. Although we might be able to bring to mind the images and conspiracy theories that have been made available since (such Abraham Zapruder’s 8 mm home movie footage of the assassination), these images were not available at the time. Mad Men as a series always strives to represent its historical milieu as authentically as possible, so the characters re-enact 22 November 1963 as authentically as possible by watching only what was on television that day (the news bulletin, Walter Kronkite’s announcement that Kennedy is dead). The contemporary backdrop to these events, including the resonances of ‘9/11’ through Mad Men, inform and collide with the authenticity on the screen.     

Revisiting <Emphasis Type="Italic">Tom Tom:</Emphasis> Performative Anamnesis and Autonomous Vision in Ken Jacobs’ Appropriations of <Emphasis Type="Italic">Tom Tom the Piper’s Son</Emphasis>

In 1969 the American avant-garde filmmaker Ken Jacobs gained wide recognition with a two-hour long interpretation of a 1905 silent short film. Ever since, the artist has kept on revisiting the same material, each time with a different technological approach. Originally hailed as a prime example of structural filmmaking, Jacobs’ more recent variations on the theme of Tom Tom the Piper’s Son beg for a broader understanding of his methods and the meanings implied. To gain a deeper insight in this on-going mise-en-abyme (and an obsession dominating a large part of his career), this essay expands comments by the artist himself with concepts taken from animation, media-archaeology and Warburg’s Mnemosyne atlas. Rereading a filmic text with minute attention, remediating it from an analogue to an electronic format, and reanimating the original action by adding a variety of intervals: all Jacobs’ strategies are aimed at demonstrating the afterlife of Tom Tom in a contemporary cultural context.     

The Documentary Real and the Shoah

Without the support of imagination, one would not have the slightest idea of the cruel ‘real’ that has occurred in the Nazi extermination camps. Yet, in documentaries imaging the events of the Shoah, one runs the risk of missing their most basic property, namely their unimaginability. The mere idea that one is able to imagine the unimaginable comes down to a denial of the Shoah’s status as an event that defies our understanding. The unimaginable ‘real’ of the Shoah, however, is not simply located in its object, in the cruelty of what happened in the camp. The Shoah makes us at the same time facing the unimaginable ‘real’ of the modern subject—the blind spot in our own identity. If we need imagination to deal with the Shoah, it is also because of an ungraspable ‘real’ in ourselves. This is why adequate Shoah representations, acknowledging their object as being beyond representation, include the same ‘beyond’ concerning the subject of the Holocaust memory. The essay makes this clear in an elaborated comparison of Claude Lanzmann’s 1985 film, Shoah, with some conceptual works of art from the late nineties—all of this ‘fine-tuned’ in a reflection upon Ingmar Bergman’s Persona.     

The Jesuits and the Method of Indivisibles

Alexander’s Infinitesimal is right to argue that the Jesuits had a chilling effect on Italian mathematics, but I question his account of the Jesuit motivations for suppressing indivisibles. Alexander alleges that the Jesuits’ intransigent commitment to Aristotle and Euclid explains their opposition to the method of indivisibles. A different hypothesis, which Alexander doesn’t pursue, is a conflict between the method of indivisibles and the Catholic doctrine of the Eucharist. This is a pity, for the conflict with the Eucharist has advantages over the Jesuit commitment to Aristotle and Euclid. The method of indivisibles was a method that developed in the course of the seventeenth century, and those who developed ‘beyond the Alps’ relied upon Aristotelian and Euclidean ideals. Alexander’s failure to recognize the importance of Aristotle and Euclid for the development of the method of indivisibles arises from an unwarranted conflation of indivisibles and infinitesimals (Sect. 2). Once indivisibles and infinitesimals are distinguished, we observe that the development of the method of indivisibles exhibits an unmistakable sympathy for Aristotle and Euclid (Sect. 3). Thus, it makes sense to consider an alternative explanation for the Jesuit abhorrence of indivisibles. And indeed, indivisibles but not infinitesimals conflict with the doctrine of the Eucharist, the central dogma of the Church (Sect. 4).     

<Emphasis Type="Italic">The Mathematical Intelligencer</Emphasis> Flunks the Olympics

The Mathematical Intelligencer recently published a note by Y. Sergeyev that challenges both mathematics and intelligence. We examine Sergeyev’s claims concerning his purported Infinity computer. We compare his grossone system with the classical Levi-Civita fields and with the hyperreal framework of A. Robinson, and analyze the related algorithmic issues inevitably arising in any genuine computer implementation. We show that Sergeyev’s grossone system is unnecessary and vague, and that whatever consistent subsystem could be salvaged is subsumed entirely within a stronger and clearer system (IST). Lou Kauffman, who published an article on a grossone, places it squarely outside the historical panorama of ideas dealing with infinity and infinitesimals.     

Evaluating Scientific Research Projects: The Units of Science in the Making

Original research is of course what scientists are expected to do. Therefore the research project is in many ways the unit of science in the making: it is the center of the professional life of the individual scientist and his coworkers. It is also the means towards the culmination of their specific activities: the original publication they hope to contribute to the scientific literature. The scientific project should therefore be of central interest to all the students of science, particularly the philosophers and sociologists of science. We shall focus on the preliminary evaluation of research projects—the specific task of referees—and will emphasize the problem of their scientificity—the chief concern of scientific gatekeepers. In the past such an examination aimed only at protecting the taxpayer from swindlers and incompetent amateurs, such as the inventors of continuous motion artifacts. In recent times a similar issue has resurfaced with regard to some of the most prestigious and most handsomely funded projects, namely work on string theory and many-worlds cosmology. Indeed, some of their faithful have claimed that these theories are so elegant, and so full of high-grade mathematics, that they should be exempted from empirical tests. This claim provoked the spirited rebuttal of the well-known cosmologists Ellis and Silk (Nature 516:321–323, 2014), which the present paper is intended to reinforce. Indeed, we shall try to show why empirical testability is necessary though insufficient for a piece of work to qualify as scientific. Finally, the present paper may also be regarded as an indirect contribution to the current debate over the reliability of quantitative indicators of scientific worth, such as the h-index of scientific productivity (e.g., Wilsdon in Nature 523:129, 2015). But we shall touch only tangentially on the sociological, political, and economics of research teams: our focus will be the acquisition of new scientific knowledge.     

Whose Agency Now?

I agree with my readers on the necessary alliance of personal agency and collective agency. My point is to prioritize the former. The reasons to prioritize the latter were excellent, and it was undoubtedly a sound decision to start with this scenario: political and institutional improvement of the collectives, enlightened by progressive social sciences. My argument for suggesting a different priority—toward personal microactions and their emergent effects—relies on the opinion that we are stuck in a sustainability crisis due to our current approach. In the question “whose agency now?”, my stress is on “now”.     

Heidegger on <Emphasis Type="Italic">Verfallenheit</Emphasis>

The question of Heidegger’s reflections on technology is explored in terms of ‘living with’ technology and including the socio-theoretical (Edinburgh) notion of ‘entanglement’ towards a review of Heidegger’s understanding of technology and media, including the entertainment industry and modern digital life. I explore Heidegger’s reflections on Gelassenheit by way of the Japanese aesthetic conception of life and of art as wabi-sabi understood with respect to Heidegger’s Gelassenheit as the art of Verfallenheit.     

The Documentary Surreal: Film and Painting in Luciano Emmer’s <Emphasis Type="Italic">La Leggenda di Sant’Orsola</Emphasis> (1948) and Henri Storck’s <Emphasis Type="Italic">Le Monde de Paul Delvaux</Emphasis> (1946)

This article deals with the aesthetics of the art documentary of the 1940s and 1950s, which can be considered as the Golden Age of the genre. Prior to the breakthrough of television in Europe, which would usurp and standardize the art documentary, cinematic reproductions of artworks resulted in experimental shorts that were highly self-reflexive. These films became visual laboratories to investigate the tensions between movement and stasis, the two- and three-dimensional, and the real and the artificial—a film on art was self-consciously presented as an art film. Focusing on La Leggenda di Sant’Orsola (1948) by Luciano Emmer and Le Monde de Paul Delvaux (1946) by Henri Storck, this article also investigates how the animation of the static image by the film medium relates to Surrealist practices.     

The Unseen Déjà-Vu: From Erkki Huhtamo’s <Emphasis Type="Italic">Topoi</Emphasis> to Ken Jacobs’ Remakes

This commentary on Edwin Carels’ essay “Revisiting Tom Tom: Performative anamnesis and autonomous vision in Ken Jacobs’ appropriations of Tom Tom the Piper’s Son” broadens up the media-archaeological framework in which Carels places his text. Notions such as Huhtamo’s topos and Zielinski’s “deep time” are brought into the discussion in order to point out the difficulty to see what there is to see and to question the position of the viewer in front of experimental films like Tom Tom the Piper’s Son and its remakes.     

On Living with Technology through Renunciation and Releasement

Marc Van den Bosche suggests that Heidegger’s conceptions of Gestell and Gelassenheit, taken together with his analysis of Nietzschean Nihilism (interpreted especially by Wolfgang Schirmacher), depicts our era in a way that “supplements” Andrew Feenberg and Don Ihde’s work. Weaving these sources together, he sees the possibility of our becoming (quoting Schirmacher) “technicians” that “live, in a released way, within the groundless.” Here, I raise some questions about whether the author has really fitted all these sources together and argue that his idea of becoming post-modern “technicians” appears to require that we first practice a very un-Heideggerian kind of “renunciation.”     

Why Axiomatize?

Axiomatization is uncommon outside mathematics, partly for being often viewed as embalming, partly because the best-known axiomatizations have serious shortcomings, and partly because it has had only one eminent champion, namely David Hilbert (Math Ann 78:405–415, 1918). The aims of this paper are (a) to describe what will be called dual axiomatics, for it concerns not just the formalism, but also the meaning (reference and sense) of the key concepts; and (b) to suggest that every instance of dual axiomatics presupposes some philosophical view or other. To illustrate these points, a theory of solidarity will be crafted and axiomatized, and certain controversies in both classical and quantum physics, as well as in the philosophy of mind, will be briefly discussed. The upshot of this paper is that dual axiomatics, unlike the purely formal axiomatics favored by the structuralists school, is not a luxury but a tool helping resolve some scientific controversies.     

Love and Realism

In this reply I try to show that, contrary to Milberry’s apparent assertion, the general intellect of the multitude does not have the explanatory robustness she accredits to it (following both Virno and the Hardt and Negri of the Empire trilogy). Digital network technologies are currently overwhelmingly effective in proletarianizing and disempowering the cognitariat and only an active technopolitics of deproletarianization could reverse this hegemonic situation. In my response to Verbeek, I attempt to correct his misinterpretation (shared by Milberry) of the Stieglerian approach as being dialectical in nature and show that, far from reinstating the humanist dichotomy between human beings and technologies, my analysis assumes their original, albeit fundamentally ambiguous and even ‘uncanny’ [unheimlich] interconnection. I conclude with pointing out some implications of this view for a ‘really realistic’ political theory of technology.