Physical superpositions exist both in classical and in quantum physics. However, what is exactly meant by ‘superposition’ in each case is extremely different. In this paper we discuss some of the multiple interpretations which exist in the literature regarding superpositions in quantum mechanics. We argue that all these interpretations have something in common: they all attempt to avoid ‘contradiction’. We argue in this paper, in favor of the importance of developing a new interpretation of superpositions which takes into account contradiction, as a key element of the formal structure of the theory, “right from the start”. In order to show the feasibility of our interpretational project we present an outline of a paraconsistent approach to quantum superpositions which attempts to account for the contradictory properties present in general within quantum superpositions. This approach must not be understood as a closed formal and conceptual scheme but rather as a first step towards a different type of understanding regarding quantum superpositions.

Providing empirically supportable instances of ontological emergence is notoriously difficult. Typically, the literature has focused on two possible sources. The first is the mind and consciousness; the second is within physics, and more specifically certain quantum effects. In this paper, I wish to suggest that the literature has overlooked a further possible instance of emergence, taken from the special science of linguistics. In particular, I will focus on the property of truth-evaluability, taken to be a property of sentences as created by the language faculty within human minds (or brains).

The intransitive cycle of superiority is characterized by such binary relations between A, B, and C that A is superior to B, B is superior to C, and C is superior to A (i.e., A>B>C>A – in contrast with transitive relations A>B>C). The first part of the article presents a brief review of studies of intransitive cycles in various disciplines (mathematics, biology, sociology, logical games, decision theory, etc.), and their reflections in educational materials. The second part of the article introduces the issue of intransitivity in elementary physics. We present principles of building mechanical intransitive devices in correspondence with the structure of the Condorcet paradox, and describe five intransitive devices: intransitive gears; levers; pulleys, wheels, and axles; wedges; inclined planes.

In this paper we investigate laziness and optimal evaluation strategies for functional programming languages. We consider the weak λ-calculus as a basis of functional programming languages, and we adapt to this setting the concepts of optimal reductions that were defined for the full λ-calculus. We prove that the usual implementation of call-by-need using sharing is optimal, that is, normalizing any λ-term with call-by-need requires exactly the same number of reduction steps as the shortest reduction sequence in the weak λ-calculus without sharing. Furthermore, we prove that optimal reduction sequences without sharing are not computable. Hence sharing is the only computable means to reach weak optimality.

Progress in science has advanced the development of human society across history, with dramatic revolutions shaped by information theory, genetic cloning, and artificial intelligence, among the many scientific achievements produced in the 20th century. However, the way that science advances itself is much less well-understood. In this work, we study the evolution of scientific development over the past century by presenting an anatomy of 89 million digitalized papers published between 1900 and 2015. We find that science has benefited from the shift from individual work to collaborative effort, with over 90% of the world-leading innovations generated by collaborations in this century, nearly four times higher than they were in the 1900s. We discover that rather than the frequent myopic- and self-referencing that was common in the early 20th century, modern scientists instead tend to look for literature further back and farther around. Finally, we also observe the globalization of scientific development from 1900 to 2015, including 25-fold and 7-fold increases in international collaborations and citations, respectively, as well as a dramatic decline in the dominant accumulation of citations by the US, the UK, and Germany, from 95% to 50% over the same period.

We equip dynamic geometry software (DGS) with a user-friendly method that enables massively parallel calculations on the graphics processing unit (GPU). This interplay of DGS and GPU opens up various applications in education and mathematical research. The GPU-aided discovery of mathematical properties, interactive visualizations of algebraic surfaces (raycasting), the mathematical deformation of images and footage in real-time, and computationally demanding numerical simulations of PDEs are examples from the long and versatile list of new domains that our approach makes accessible within a DGS. We ease the development of complex (mathematical) visualizations and provide a rapid-prototyping scheme for general-purpose computations (GPGPU). The possibility to program both CPU and GPU with the use of only one high-level (scripting) programming language is a crucial aspect of our concept.

Various methods have been proposed for transporting large probes or colony ships through interstellar space to nearby stellar neighborhoods. All methods proposed thus far encounter monumental technological or engineering roadblocks, or even rely on speculative unknown science. In particular light of the recent public excitement and ensuing disappointment regarding the exotic “EM drive” we feel it worthwhile to point out that propellantless space travel is eminently possible based on well established physical principles. We propose a new mode of transport which relies on electric-field moderated momentum exchange with the ionized particles in the interstellar medium. While the application of this mechanism faces significant challenges requiring industrial-scale exploitation of space, the technological roadblocks are minimal, and are perhaps more easily addressed than the issues presented by light sails or particle beam powered craft.

Although black holes are objects of central importance across many fields of physics, there is no agreed upon definition for them, a fact that does not seem to be widely recognized. Physicists in different fields conceive of and reason about them in radically different, and often conflicting, ways. All those ways, however, seem sound in the relevant contexts. After examining and comparing many of the definitions used in practice, I consider the problems that the lack of a universally accepted definition leads to, and discuss whether one is in fact needed for progress in the physics of black holes. I conclude that, within reasonable bounds, the profusion of different definitions is in fact a virtue, making the investigation of black holes possible and fruitful in all the many different kinds of problems about them that physicists consider, although one must take care in trying to translate results between fields.

Reverse mathematics studies which subsystems of second order arithmetic are equivalent to key theorems of ordinary, non-set-theoretic mathematics. The main philosophical application of reverse mathematics proposed thus far is foundational analysis, which explores the limits of different foundations for mathematics in a formally precise manner. This paper gives a detailed account of the motivations and methodology of foundational analysis, which have heretofore been largely left implicit in the practice. It then shows how this account can be fruitfully applied in the evaluation of major foundational approaches by a careful examination of two case studies: a partial realization of Hilbert’s program due to Simpson [1988], and predicativism in the extended form due to Feferman and Schutte. Shore [2010, 2013] proposes that equivalences in reverse mathematics be proved in the same way as inequivalences, namely by considering only ω -models of the systems in question.

This is a brief, popular-level introduction to holographic entanglement. It was published in the newsletter of the International Centre for Theoretical Sciences, Bangalore.