The purpose of this article is to integrate two outstanding problems within the philosophy of science. The first concerns what role aesthetics plays in scientific thinking. The second is the problem of how logically testable ideas are generated (the so-called "psychology of research" versus "logic of (dis)proof" problem). I argue that aesthetic sensibility is the basis for what scientists often call intuition, and that intuition in turn embodies (in a literal physiological sense) ways of thinking that have their own meta-logic. (...) Thus, aesthetics is a form of cognition. Scientists think not in equations or words or other logical abstractions, but emotionally and sensually, using visual and aural images, kinesthetic and other proprioceptive feelings, sensations, patterns, and analogies. These aesthetic forms of thinking have their own logics that I call "synosia", from the root words synaesthesia (a combining of senses) and gnosis, "to know". Synosia denotes understanding that integrates feeling that one knows with feeling what one knows. Eminent scientists universally describe an explicitly secondary process in which such personal knowledge must be "translated" into a formal language, such as words or equations, in order to be communicated to other people. Many of the unsolved problems that philosophers of science (as well as psychologists and artificial intelligence researchers) have had in making sense of scientific thinking have arisen from confusing the form and content of the final translations with the hidden means by which scientific insights are actually achieved. (shrink)

Volterra's (1926) equations for competition and predator-prey interactions are modified by introduction of root terms. A critical comparison with the original equations shows that the dynamic properties of the systems remain essentially alike, while the modification allows for explicit solution of the differential equations. Detailed solutions and numerical examples are given.

This paper provides equational semantics for Dung's argumentation networks. The network nodes get numerical values in [0,1], and are supposed to satisfy certain equations. The solutions to these equations correspond to the ?extensions? of the network. This approach is very general and includes the Caminada labelling as a special case, as well as many other so-called network extensions, support systems, higher level attacks, Boolean networks, dependence on time, and much more. The equational approach has its conceptual roots in (...) the nineteenth century following the algebraic equational approach to logic by George Boole, Louis Couturat, and Ernst Schroeder. (shrink)

Objective Moral distress is a complex phenomenon experienced by healthcare professionals. This study examined the relationships between key dimensions of Organizational Culture in Healthcare (OCHC)—perceived psychological safety, ethical climate, patient safety—and healthcare professionals’ perception of moral distress.Design Cross-sectional surveySetting Pediatric and adult critical care medicine, and adult hospital medicine healthcare professionals in the United States.Participants Physicians (n = 260), nurses (n = 256), and advanced practice providers (n = 110) participated in the study.Main outcome measures Three dimensions of OCHC were (...) measured using validated questionnaires: Olson’s Hospital Ethical Climate Survey, Agency for Healthcare Research and Quality’s Patient Safety Culture Survey, and Edmondson’s Team Psychological Safety Survey. The perception of moral distress was measured using the Moral Distress Amidst a Pandemic Survey. The hypothesized relationships between various dimensions were tested with structural equation modeling (SEM).Results Adequate model fit was achieved in the SEM: a root-mean-square error of approximation =0.072 (90% CI 0.069 to 0.075), standardized root mean square residual = 0.056, and comparative fit index =0.926. Perceived psychological safety (β= −0.357, p <.001) and patient safety culture (β = −0.428, p<.001) were negatively related to moral distress experience. There was no significant association between ethical climate and moral distress (β = 0.106, p = 0.319). Ethical Climate, however, was highly correlated with Patient Safety Culture (factor correlation= 0.82).Conclusions We used structural equation model to test a theoretical model of multi-dimensional organizational culture and healthcare climate (OCHC) and moral distress.Significant associations were found, supporting mitigating strategies to optimize psychological safety and patient safety culture to address moral distress among healthcare professionals. Future initiatives and studies should account for key dimensions of OCHC with multi-pronged targets to preserve the moral well-being of individuals, teams, and organizations. (shrink)

It is shown in this article that the two sides of an equation in the medieval Arabic algebra are aggregations of the algebraic “numbers” (powers) with no operations present. Unlike an expression such as our 3x + 4, the Arabic polynomial “three things and four dirhams” is merely a collection of seven objects of two different types. Ideally, the two sides of an equation were polynomials so the Arabic algebraists preferred to work out all operations of the enunciation to a (...) problem before stating an equation. Some difficult problems which involve square roots and divisions cannot be handled nicely by this basic method, so we do find square roots of polynomials and expressions of the form “A divided by B” in some equations. But rather than initiate a reconsideration of the notion of equation, these developments were used only for particularly complex problems. Also, the algebraic notation practiced in the Maghreb in the later middle ages was developed with the “aggregations” interpretation in mind, so it had no noticeable impact on the concept of polynomial. Arabic algebraists continued to solve problems by working operations before setting up an equation to the end of the medieval period. (shrink)

Multivariate behavioral research often focuses on latent constructs—such as motivation, self-concept, or wellbeing—that cannot be directly observed. Typically, these latent constructs are measured with items in standardized instruments. To test the factorial structure and multidimensionality of latent constructs in educational and psychological research, Morin et al. proposed bifactor exploratory structural equation modeling. This meta-analytic review aimed to estimate the extent to which B-ESEM model fit differs from other model representations, including confirmatory factor analysis, exploratory structural equation modeling, hierarchical CFA, hierarchical (...) ESEM, and bifactor-CFA. The study domains included learning and instruction, motivation and emotion, self and identity, depression and wellbeing, and interpersonal relations. The meta-analyzed fit indices were the χ2/df ratio, the comparative fit index, the Tucker-Lewis index, the root mean square error of approximation, and the standardized root mean squared residual. The findings of this meta-analytic review indicate that the B-ESEM model fit is superior to the fit of reference models. Furthermore, the results suggest that model fit is sensitive to sample size, item number, and the number of specific and general factors in a model. (shrink)

The progress of Mathematics during the nineteenth century was characterised both by an enormous acquisition of new knowledge and by the attempts to introduce rigour in reasoning patterns and mathematical writing. Cauchy’s presentation of Mathematical Analysis was not immediately accepted, and many writers, though aware of that new style, did not use it in their own mathematical production. This paper is devoted to an episode of this sort that took place in Spain during the first half of the century: It (...) deals with the presentation of a method for numerically solving algebraic equations by José Mariano Vallejo, a late Spanish follower of the Enlightenment ideas, politician, writer, and mathematician who published it in the fourth (1840) edition of his book Compendio de Matemáticas Puras y Mistas, claiming to have discovered it on his own. Vallejo’s main achievement was to write down the whole procedure in a very careful way taking into account the different types of roots, although he paid little attention to questions such as convergence checks and the fulfilment of the hypotheses of Rolle’s Theorem. For sure this lack of mathematical care prevented Vallejo to occupy a place among the forerunners of Computational Algebra. (shrink)

Abstract In this paper an algebraic method is presented to derive a 4 × 4 Hermitian Schrödinger equation from with and . The latter operator replacement is a common procedure in a quantum description of the total energy. In the derivation we don’t make use of Dirac’s method of four vectors. Moreover, the root operator isn’t squared either. Instead, use is made of the algebra of operators to derive a Hermitian matrix Schrödinger equation. We believe that new physics can (...) be obtained from an alternative quantization of the relativistic total energy. Note e.g. the pion physics behind the Klein–Gordon equation and the antimatter behind the Dirac quantization of the total relativistic energy. In this paper, for the sake of clarity, a time-only dependence of the electromagnetic potential vector is assumed. It is also demonstrated that a “latent” Lorentz invariance exists related to a derived expression for amplitude and phase. (shrink)

Background: Forgiveness has the potential to resolve painful feelings arising from nurse–patient conflicts. It would be useful to evaluate direct and indirect important factors which are related to forgiveness in order to design interventions that try to facilitate forgiveness. Aim/objective: The purpose of this study was to evaluate the intermediating role of empathy in the cultural competence–forgiveness association among nurses using structural equation modeling. Research design: The research applied a cross-sectional correlational design. Participants and research context: The study included 380 (...) nurses eight hospitals in southern Iran. Ethical considerations: The Ethics and Research Committee of Birjand University of Medical Sciences approved the study protocol. The voluntary nature of participation was explained consent was obtained from participants, and anonymity was guaranteed. Findings: Most of the participants were married and female and fell in the 20- to 30-year-old category. Most of them (89.5%) had a working experience of 1–10 years. The proposed model showed that nurses’ empathy intermediated the association between nurses’ cultural competence and forgiveness which has fitted the data acceptably (root mean square error approximation = 0.070; comparative fit index = 0.993; goodness-of-fit index = 0.983; and χ2/df = 2.85). Conclusion: Empathy skills and cultural competence training were essential for interventions aimed at increasing the tendency to forgive patients. In such interventions, planners should aim at increasing nurses’ cultural competence in order to enhance their empathy toward patients, which can, in turn, lead to a greater wish to forgive patients. (shrink)

ArgumentThe study of algebra in China has often focused on the algebraic “procedure of the Celestial Source.” Its geometrical ancestors are less known. TheYigu yanduan, authored by Li Ye (1192-1279), presents the procedure alongside its two geometrical counterparts, the “Section of Pieces [of Areas]” and the “Old Procedure.” The three procedures are known to represent three generations of algorithms used to set up quadratic equations. A similar geometrical procedure appears in a treatise written by Yang Hui (second half of (...) thirteenth century). Although the procedures look alike at first glance, the two treatises reveal different moments in their work on the relation between counting materials and geometrical representation. This study challenges their chronology trying to identify the meander of the geometrical roots of the Celestial Source. The construction of negative coefficients plays a pivotal role in this mutation and shows several layers of composition. (shrink)

Relativistic geometrical action for a quantum particle in the superspace is analyzed from theoretical group point of view. To this end an alternative technique of quantization outlined by the authors in a previous work and that is based in the correct interpretation of the square root Hamiltonian, is used. The obtained spectrum of physical states and the Fock construction consist of Squeezed States which correspond to the representations with the lowest weights $\lambda=\frac{1}{4}$ and $\lambda=\frac{3}{4}$ with four possible (non-trivial) fractional (...) representations for the group decomposition of the spin structure. From the theory of semigroups the analytical representation of the radical operator in the superspace is constructed, the conserved currents are computed and a new relativistic wave equation is proposed and explicitly solved for the time-dependent case. The relation with the Relativistic Schrödinger equation and the Time-dependent Harmonic Oscillator is analyzed and discussed. (shrink)

Abstract:Western business philosophy is rooted in the concepts of free enterprise, free markets, free choice. Yet freedom has its limits. Nature itself imposes constraints. In the state of nature each business must try to accomplish everything autonomously and ward off the attacks of rivals. These activities cost the business a great deal of freedom. The social contract emerges from such anarchy to increase the freedom available to all members of society. It does so by setting limits on individual freedom which (...) actually increase the overall amount of freedom available within the system. The Social Equation presents a relational model of this contract to show how overall freedom is increased in a state of society. In so doing, the obligations which society places on businesses to produce beneficial goods and services is developed. Next, the complex relationship between socially enforced constraints and social moral constraints is examined, showing that social moral constraints increase freedom more than do enforced constraints. This work concludes with proposed uses of the Social Equation as a heuristic for business ethics. (shrink)

This cross-sectional study aimed to assess the applicability of social cognitive determinants among the Chinese adolescents and examine whether the predictability of the social cognitive theory model on physical activity differs across gender and urbanization. A total of 3,000 Chinese adolescents ranging between the ages of 12–15 years were randomly selected to complete a set of questionnaires. Structural equation modeling was applied to investigate the relationships between social cognitive variables and PA in the urbanization and gender subgroups. The overall model (...) explained 38.9% of the variance in PA. Fit indices indicated that the structural model of SCT was good: root mean square error of approximation = 0.047, RMR = 0.028, goodness of fit index = 0.974, adjusted goodness of fit index = 0.960, Tucker–Lewis coefficient = 0.971, and comparative fit index = 0.978. Regarding the subgroup analysis, social support had a more substantial impact on the PA of adolescents in suburban areas than that in urban areas, whereas self-regulation had a more substantial impact on the PA of adolescents in urban areas than in suburban areas. The results indicate that the SCT model predicts the PA of Chinese adolescents substantially. An SCT model could apply over a range of subgroups to predict the PA behavior and should be considered comprehensively when designing interventions. These findings would benefit PA among the Chinese adolescents, especially across genders and urbanization. (shrink)

This paper is a review of the canonical proper-time approach to relativistic mechanics and classical electrodynamics. The purpose is to provide a physically complete classical background for a new approach to relativistic quantum theory. Here, we first show that there are two versions of Maxwell’s equations. The new version fixes the clock of the field source for all inertial observers. However now, the (natural definition of the effective) speed of light is no longer an invariant for all observers, but (...) depends on the motion of the source. This approach allows us to account for radiation reaction without the Lorentz-Dirac equation, self-energy (divergence), advanced potentials or any assumptions about the structure of the source. The theory provides a new invariance group which, in general, is a nonlinear and nonlocal representation of the Lorentz group. This approach also provides a natural (and unique) definition of simultaneity for all observers.The corresponding particle theory is independent of particle number, noninvariant under time reversal (arrow of time), compatible with quantum mechanics and has a corresponding positive definite canonical Hamiltonian associated with the clock of the source.We also provide a brief review of our work on the foundational aspects of the corresponding relativistic quantum theory. Here, we show that the standard square-root and Dirac equations are actually two distinct spin- $\frac{1}{2}$ particle equations. (shrink)

Ibn al-Zarqālluh (al-Andalus, d. 1100) introduced a new inequality in the longitudinal motion of the Moon into Ptolemy’s lunar model with the amplitude of 24′, which periodically changes in terms of a sine function with the distance in longitude between the mean Moon and the solar apogee as the variable. It can be shown that the discovery had its roots in his examination of the discrepancies between the times of the lunar eclipses he obtained from the data of his eclipse (...) observations over a 37-year period in the latter part of the eleventh century and the predictions made on the basis of the lunar theories in the Mumta $$\textit{\d{h}}$$ an zīj (Baghdad, ca. 830) and al-Battānī’s zīj (Raqqa, d. 929), which were available to him at the time. What Ibn al-Zarqālluh found is, in fact, a special case of the annual equation of the Moon, which is applicable in the oppositions and, thus, in the lunar eclipses. The inequality was discovered independently by Tycho Brahe (d. 1601) and Johannes Kepler (d. 1630). As Ibn Yūnus (d. 1009) reports in his $$\textit{\d{H}}$$ ākimī zīj, Ibn al-Zarqālluh’s medieval Middle Eastern predecessors, the Persian astronomers Māhānī (d. ca. 880) and Nayrīzī (d. 922) as well as ‘Alī b. Amājūr (fl. ca. 920), were already acquainted with the problem of the eclipse timing errors, but it had remained unresolved until Ibn Yūnus provided a provisional, and incorrect, solution by reducing the size of the lunar epicycle. As we argue, the diverse ways to tackle the same problem stem from two different methodologies in astronomical reasoning in the traditions developed separately in the Eastern and Western regions of the medieval Islamic domain. (shrink)

We discuss the role of linguistic metaphors as a cognitive frame for the understanding of genetic information processing. The essential similarity between language and genetic information processing has been recognized since the very beginning, and many prominent scholars have noted the possibility of considering genes and genomes as texts or languages. Most of the core terms in molecular biology are based on linguistic metaphors. The processing of genetic information is understood as some operations on text – writing, reading and editing (...) and their specification (encoding/decoding, proofreading, transcription, translation, reading frame). The concept of gene reading can be traced from the archaic idea of the equation of Life and Nature with the Book. Thus, the genetics itself can be metaphorically represented as some operations on text (deciphering, understanding, codebreaking, transcribing, editing, etc.), which are performed by scientists. At the same time linguistic metaphors portrayed gene entities also as having the ability of reading. In the case of such “bio-reading” some essential features similar to the processes of human reading can be revealed: this is an ability to identify the biochemical sequences based on their function in an abstract system and distinguish between type and its contextual tokens of the same type. Metaphors seem to be an effective instrument for representation, as they make possible a two-dimensional description: biochemical by its experimental empirical results and textual based on the cognitive models of comprehension. In addition to their heuristic value, linguistic metaphors are based on the essential characteristics of genetic information derived from its dual nature: biochemical by its substance, textual (or quasi-textual) by its formal organization. It can be concluded that linguistic metaphors denoting biochemical objects and processes seem to be a method of description and explanation of these heterogeneous properties. (shrink)

We discuss the role of linguistic metaphors as a cognitive frame for the understanding of genetic information processing. The essential similarity between language and genetic information processing has been recognized since the very beginning, and many prominent scholars have noted the possibility of considering genes and genomes as texts or languages. Most of the core terms in molecular biology are based on linguistic metaphors. The processing of genetic information is understood as some operations on text – writing, reading and editing (...) and their specification (encoding/decoding, proofreading, transcription, translation, reading frame). The concept of gene reading can be traced from the archaic idea of the equation of Life and Nature with the Book. Thus, the genetics itself can be metaphorically represented as some operations on text (deciphering, understanding, codebreaking, transcribing, editing, etc.), which are performed by scientists. At the same time linguistic metaphors portrayed gene entities also as having the ability of reading. In the case of such “bio-reading” some essential features similar to the processes of human reading can be revealed: this is an ability to identify the biochemical sequences based on their function in an abstract system and distinguish between type and its contextual tokens of the same type. Metaphors seem to be an effective instrument for representation, as they make possible a two-dimensional description: biochemical by its experimental empirical results and textual according to the cognitive models of comprehension. In addition to their heuristic value, linguistic metaphors are based on the essential characteristics of genetic information derived from its dual nature: biochemical by its substance, textual (or quasitextual) by its formal organization. It can be concluded that linguistic metaphors denoting biochemical objects and processes seem to be a method of description and explanation of these heterogeneous properties. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Art as Occupations:Two Neglected Roots of John Dewey's AestheticsAuthors: Fabio Campeotto (Consejo Nacional de Investigaciones Científicas y Técnicas, CONICET, Univ. Nacional de La Rioja); Juan Manuel Saharrea (CONICET, Universidad Católica de Córdoba-Unidad Asociada al CONICET) and Claudio M. Viale (CONICET, Universidad Católica de Córdoba-Unidad Asociada al CONICET). Campeotto and Saharrea contributed similarly to the development of this work. Language edition: Rita Karina Plascencia, https://www.rkplasencia.com/. This article was made in (...) the frame of two research projects: "Pragmatismo y educación: Fundamentos teóricos y abordajes empíricos," financed by the Universidad Católica de Córdoba (2019–2023); and "Praxis, experimentalismo, aprendizaje y democracia: hacia una reevaluación de la filosofía de la educación contemporánea," PICT 2020 serie A 01539 financed by the Fondo para la Investigación Científica y Tecnológica (FONCyT). Both projects were under the direction of C. M. Viale.undoubtedly, art as experience1 is one of the most important texts by John Dewey, as well as his most systematic approach to aesthetics.2 This book usually appears in the literature as an almost mandatory reading for interpreters of classical pragmatism, and it is praised as an ineludible reference for those interested in aesthetics from a pragmatic point of view. However, this justified centrality tends to invisibilize two important veins of Dewey's thought: the vital role of his fragmentary or piecemeal approach to aesthetics, on one hand, and the relevance of his educational conceptions in relation to aesthetics, on the other.Going beyond the centrality of Art as Experience toward a comprehensive and contemporary view of Dewey's aesthetics entails looking upon three elements of his thought: Firstly, Dewey's works—some of them considered minor and some implicit or sporadic references in canonical texts—depicting the links between education and aesthetics in his philosophy as well as texts that belong to his fragmentary approach to aesthetics. Secondly, his systematic development of aesthetics, mainly in Art as Experience, where Dewey presents his conceptions at length. Thirdly, what we could call a re-evaluated aesthetics, which consists in a contemporary attempt to integrate diverse aspects of his philosophy, trying to overcome some weaknesses in his theoretical developments, especially regarding his dealing with the links between education and [End Page 1] aesthetics. It is necessary to remark that these links were neither adequately addressed by Dewey nor exhaustively examined by the literature, as far as we know. We hold that it is crucial to make them critically explicit, in order to get fruitful contemporary approaches not only to Dewey's aesthetics but also to his pedagogy and philosophy of education.Thus, the core question of this article is the following: How should the educational root of Dewey's aesthetics have worked? Or, more precisely, how should he have explicitly or meticulously conceived aesthetics in relation to his educational developments? We think that two neglected roots of Dewey's writings related to aesthetics can help us to re-evaluate it: what we call its fragmentary approach and Albert C. Barnes's role in it, on one hand, and a coherent articulation among occupation, art teaching, and the overcoming of the distinction between vocational and humanistic education, on the other.To carry out our task, we have divided this article into three parts. In the first (The Genesis of Dewey's Aesthetics: A Re-interpretation), we argue how to interpret the emergence of Dewey's aesthetics. In the second (Dewey and Education: Central Issues), we present the key aspects of this topic related to our purposes. In the third section (Two Neglected Roots of Dewey's Aesthetics), we develop our argument by describing how to recover these sources, and also by showing how Dewey's aesthetics could be critically re-evaluated or reconstructed from a contemporary viewpoint. Finally, we put forward a conclusion.The Genesis of Dewey's Aesthetics: A Re-interpretationIt is well-known that Dewey's aesthetics is usually equated with Art as Experience. This is part of the canonical interpretations that tend to conceive Dewey's philosophy in, using his term, grooves (LW 2:113). Democracy and Education... (shrink)

We discuss the role of linguistic metaphors as a cognitive frame for the understanding of genetic information processing. The essential similarity between language and genetic information processing has been recognized since the very beginning, and many prominent scholars have noted the possibility of considering genes and genomes as texts or languages. Most of the core terms in molecular biology are based on linguistic metaphors. The processing of genetic information is understood as some operations on text – writing, reading and editing (...) and their specification (encoding/decoding, proofreading, transcription, translation, reading frame). The concept of gene reading can be traced from the archaic idea of the equation of Life and Nature with the Book. Thus, the genetics itself can be metaphorically represented as some operations on text (deciphering, understanding, code-breaking, transcribing, editing, etc.), which are performed by scientists. At the same time linguistic metaphors portrayed gene entities also as having the ability of reading. In the case of such “bio-reading” some essential features similar to the processes of human reading can be revealed: this is an ability to identify the biochemical sequences based on their function in an abstract system and distinguish between type and its contextual tokens of the same type. Metaphors seem to be an effective instrument for representation, as they make possible a two-dimensional description: biochemical by its experimental empirical results and textual based on the cognitive models of comprehension. In addition to their heuristic value, linguistic metaphors are based on the essential characteristics of genetic information derived from its dual nature: biochemical by its substance, textual (or quasi-textual) by its formal organization. It can be concluded that linguistic metaphors denoting biochemical objects and processes seem to be a method of description and explanation of these heterogeneous properties. (shrink)

In this 1835 work, Sarah Porter, née Ricardo shows her enthusiasm for arithmetic, and her concern for teaching it in a way that will develop the pupil's mind: 'There is no branch of early education so admirably adapted to call forth and strengthen the reasoning powers.' She uses the device of a conversation between pupil and teacher, popularised by Jane Marcet, to guide young Edmund from the written symbols for numbers through addition, subtraction, multiplication and division, fractions and decimals, proportion, (...) and square and cube roots. Answers to the questions are provided at the end of the book. A member of the Central Society of Education, which promoted imaginative theories of education instead of rote learning, Mrs Porter reworked her book in 1852 as Rational Arithmetic, a more conventional and less entertaining textbook for use in schools. (shrink)

The problem of rationalizing denominators for two types of fractions is discussed in the paper. By using the theory and algorithms of Gröbner bases, we first introduce a method to rationalize the denominators of fractions with square root and cube root, and then, for the denominators with higher radical of the general form, the problem of rationalizing denominators is converted into the related problem of finding the minimal polynomials. Some interesting results and an executable algorithm for rationalizing (...) the denominator of these type fractions are presented. Furthermore, an example is also established to illustrate the effectiveness of the algorithm. (shrink)

If Pegasus existed, he would indeed be in space and time, but only because the word ‘Pegasus’ has spatio-temporal connotations, and not because ‘exists’ has spatio-temporal connotations. If spatio-temporal reference is lacking when we affirm the existence of the cube root of 27, that is simply because a cube root is not a spatio-temporal kind of thing.

Nature's simplest atom and mother of all matter, hydrogen feeds the stars as well as interlaces the molecules of their biological descendants – to whom it ultimately whispers the secrets of quantum reality. Hydrogen’s most prevalent earthly guise lies within the composition of water. A slight electrical disturbance can split water into hydrogen and oxygen gas, resulting in diaphanous bubble clouds slowly rising towards the liquid’s surface. Though the founding fathers of electrochemistry posited that the mass of liberated bubbles is (...) directly proportional to the input voltage, certain modes of electrolysis release more energy than is spent. One such mode involves water’s Janus-faced capacity to react as either an acid or a base. Emanating from an array of electrodes at the bottom of a water-filled chamber, strings and strata of hydrogen bubbles meticulously trace their emergent surroundings. In addition to eddy formations incited by a bubble's rapid growth and subsequent detachment from the electrode surface, acoustic vibrations permeate the two-phase fluid. As the sonic frequency and amplitude rises, the hydrogen bubbles start to coalesce with one another. When the sound field reaches maximum intensity, it can trap bubbles within its antinodes. The vibrations are generated both by transducers and by the bubbles themselves, which emit frequencies ranging from the audible spectrum to as high as 800 kHz. A white laser sheet scans and illuminates the hydrogen bubble trajectories. Each quivering bubble-lens divides the white light into its constituent spectrum of colors. While scanning, the laser sheet also swiftly pulsates and thereby extends the perceivable resolution of micro-momentary bubble dynamics. Before it even begins to map out its vibratory environment, a bubble goes through various stages of spatio-temporal evolution. During the first phase of growth, a bubble nucleus inflates linearly with time. At the second stage, bubble growth is limited by the diffusion of gas within the liquid, causing its size to increase as the square root of time. The final phase before detachment is limited by the kinetics of dissolved gas production, causing the bubble to grow as the cube root of time.1 Beyond macroscopically observable bubbles, an expanse of nanobubbles hides within the water’s internal architecture. Some researchers presume that these nanobubbles of dissolved gas are the carriers of water’s magnetic ‘memory’, enabling electromagnetic fields to saturate its innards for hours and even days after their initial appearance. In the seas and oceans, the lingering presence of electromagnetic fields photonically imparted by sunlight, triggers the electrolysis responsible for most of the Earth’s hydrogen. An essential form of photosynthesis, solar water splitting is the cleanest and most efficient means imaginable for generating and storing energy. —Evelina Domnitch & Dmitry Gelfand *** Animals and plants are formed in earth and in water because there is water in earth, and there is pneuma in water, and there is soul heat in all pneuma ; so that in a way all things are full of soul. Hence plants and animals quickly form once this gets enclosed; and when this enclosing happens, when the corporeal liquids get heated, a sort of frothy bubble is formed. Now the difference between the various creatures which are produced in this way are due to the stuff which makes up the envelope around the soul-source.2 Throwing light into this pneumatic spray of perdurances, which would otherwise swarm below the threshold of human visibility, Evelina Domnitch and Dmitry Gelfand’s Hydrogeny saturates the viewer’s sensorial space with the nano-architectures of froth. Straddling the cell wall between scientific enquiry and artistic praxis, Hydrogeny , beckons a recasting of Lucretius' clinamen in tune with the technologies of the modern observer. For Lucretius it was the indeterminate swerving of an atomistic layer of reality which accounted for the unpredictability of change and the existence of free will. Taken up by Harold Bloom to describe the swerving of cultural production from that which has already been made, the idea has since been textually redressed by Lacan, Derrida, Serres, Deleuze, Nancy, and Badiou. Here we have been given a kaleidoscopic technique for refining and expanding awareness of our enmeshment with so many nested, atomistic layers of object-bubbles—of things—as Aristotle might say,“full of soul.” The gravitational pull of Hydrogeny ushers a de-centered human spectatorship to the ever more intimate recesses of what media philosopher N. Katherine Hayles calls our capacity for “deep attention.”3 Vaporous attention suspended and re-oriented. Microscopic as these diaphanous waves are, the calling they produce is anything but inconsequential. Evelina Domnitch and Dmitry Gelfand are two-thirds of the Amsterdam-based Art–Science Labratory, Optofonica , an atelier initiated by the Italian interdisciplinary artist TeZ in 2006. Follow more of their work at www.portablepalace.com —Isaac Linder NOTES (1) cf. Brandon, Kelsall, Levine, & Smith. “Interfacial Electrical Properties of Electrogenerated Bubbles.” Journal of Applied Electrochemistry 15 (1985):485-493. (2)Aristotle, On the Generation of Animals, 762a18, tr. A. L. Peck (Cambridge, MA: Loeb Classical Library, 1942). (3)“ My article on hyper and deep attention ,” N. Katherine Hayles, accessed on September 14, 2011. (shrink)

Everything you wanted to know about direct reference and always dared to ask is contained in Recanati's new book, which is not only a comprehensive survey on the received doctrine but also an original attempt to find a new way out of the many puzzles which surround the "new theory of reference" (in H. Wettstein's words) since its origins. Principles and conceptions are indeed acutely specified and Recanati's own theses are argued for in a very subtle and rigorous way. One (...) cannot leave the volume without the impression that his understanding of the subject has been radically deepened and enlightened. A thorough analysis of such a detailed work would probably need a paper as long as the volume itself. Thus, I will limit myself to reconstruct three general aims of the book and to discuss some of the issues they raise. These aims are: i) to find a new criterion for the referentiality of directly referential terms (from now on, DR terms); ii) to develop a multi-layered pragmatics which allows one to deal pragmatically with what has been hitherto considered as belonging to a semantic layer only; iii) to put forward a truth-conditional pragmatic analysis of belief reports which accounts for the semantic import of the non truth-conditional thought underlying a linguistic utterance. Let me deal with i) first. Recanati puts forward a criterion of referentiality which in his mind allows one to tell de jure rigid designators (names, indexicals: what we have above labeled DR terms) from de facto ones (definite descriptions such as "the cube root of 27"). The former, not the latter, directly designate their referent since they are type-referential. He defines type-referentiality as follows: A term is (type)-referential if and only if its linguistic meaning includes a feature, call it 'REF', by virtue of which it indicates that the truth-condition ... of the utterance where it occurs is singular. (p.17) Suppose we take the following two utterances, "3 is odd" and "The cube root of 27 is odd", where the former contains a de jure, the latter a de facto, rigid designator. Although both utterances have singular truth-conditions, let us say are associated with a singular proposition to the effect that the number 3 is odd, the former, but not the latter, presents itself as true iff 3 is odd, i.e.. (shrink)

An MV-algebra A=(A,0,¬,⊕) is an abelian monoid (A,0,⊕) equipped with a unary operation ¬ such that ¬¬x=x,x⊕¬0=¬0, and y⊕¬(y⊕¬x)=x⊕¬(x⊕¬y). Chang proved that the equational class of MV-algebras is generated by the real unit interval [0,1] equipped with the operations ¬x=1−x and x⊕y=min(1,x+y). Therefore, the free n-generated MV-algebra Free n is the algebra of [0,1]-valued functions over the n-cube [0,1] n generated by the coordinate functions ξ i ,i=1, . . . ,n, with pointwise operations. Any such function f is (...) a McNaughton function, i.e., f is continuous, piecewise linear, and each piece has integer coefficients. Conversely, McNaughton proved that all McNaughton functions f: [0,1] n →[0,1] are in Free n . The elements of Free n are logical equivalence classes of n-variable formulas in the infinite-valued calculus of Łukasiewicz. The aim of this paper is to provide an alternative, representation-free, characterization of Free n. (shrink)

Rooted in theory of planned behavior (TPB) supplemented with self-determination theory (SDT), this study explores determinants of willingness to receive and provide resources in Europe's non-remunerated and remunerated collaborative consumption (CC). The exploration was conducted within a single research model by assessing the role of (a) TPB constructs reflecting attitude towards participation in CC, perceived social pressure to engage, and perceived level of difficulty that engagement requires and (b) SDT constructs of environmental, social, and economic motives for participation. The data (...) were collected through an online questionnaire, and the structural relationships were analyzed using structural equation modeling. Willingness to consume in non-remunerated and remunerated CC was positively directly influenced by social pressure to engage in CC and participation being perceived as pleasant, negatively by the level of difficulty that engagement requires, as well as positively indirectly influenced by environmental concern and sociability. Additionally, environmental concern had positive direct effect on willingness to consume only in the remunerated context. Willingness to provide in non-remunerated CC was positively directly influenced by perceiving participation as pleasant and indirectly by environmental concern and sociability. Resource provision in remunerated CC was not explained by any of the determinants. (shrink)

Treating the existential quantification ∃ν i as a diamond $\diamond_i$ and the identity ν i = ν j as a constant δ ij , we study restricted versions of first order logic as if they were modal formalisms. This approach is closely related to algebraic logic, as the Kripke frames of our system have the type of the atom structures of cylindric algebras; the full cylindric set algebras are the complex algebras of the intended multidimensional frames called cubes. The main (...) contribution of the paper is a characterization of these cube frames for the finite-dimensional case and, as a consequence of the special form of this characterization, a completeness theorem for this class. These results lead to finite, though unorthodox, derivation systems for several related formalisms, e.g. for the valid n-variable first order formulas, for type-free valid formulas and for the equational theory of representable cylindric algebras. The result for type-free valid formulas indicates a positive solution to Problem 4.16 of Henkin, Monk and Tarski [16]. (shrink)

Many philosophers have equated the denial of foundationalism with a call for coherentist approaches to epistemology. I think such equations are spurious, and to show why this is so I contrast the views of a paradigmatic coherentist with an antifoundationalist alternative. This article examines the coherentism of Laurence BonJour with an eye toward the way in which BonJour's views fail to fully adopt the insights of their Sellarsian roots. In particular, I argue that BonJour's view endorses the philosophy of (...) mind that Wilfrid Sellars criticized in "Empiricism and the Philosophy of Mind" - which itself may be no sin , but is a problem given BonJour's express sympathies with Sellars and EPM. I begin by contrasting the approaches taken by BonJour in The Structure of Empirical Knowledge and by Sellars in EPM, arguing that one could deny foundationalism without, thereby, becoming a coherentist. (shrink)

We introduce a sequent calculus B for a new logic, named basic logic. The aim of basic logic is to find a structure in the space of logics. Classical, intuitionistic, quantum and non-modal linear logics, are all obtained as extensions in a uniform way and in a single framework. We isolate three properties, which characterize B positively: reflection, symmetry and visibility. A logical constant obeys to the principle of reflection if it is characterized semantically by an equation binding it with (...) a metalinguistic link between assertions, and if its syntactic inference rules are obtained by solving that equation. All connectives of basic logic satisfy reflection. To the control of weakening and contraction of linear logic, basic logic adds a strict control of contexts, by requiring that all active formulae in all rules are isolated, that is visible. From visibility, cut-elimination follows. The full, geometric symmetry of basic logic induces known symmetries of its extensions, and adds a symmetry among them, producing the structure of a cube. (shrink)

Research into the roots of ideological extremism has traditionally focused on the social, economic, and demographic factors that make people vulnerable to adopting hostile attitudes toward outgroups. However, there is insufficient empirical work on individual differences in implicit cognition and information processing styles that amplify an individual’s susceptibility to endorsing violence to protect an ideological cause or group. Here we present original evidence that objectively assessed cognitive inflexibility predicts extremist attitudes, including a willingness to harm others, and sacrifice one’s life (...) for the group. Across two samples (N = 1,047) from the United Kingdom and United States, structural equation models demonstrated that cognitive inflexibility predicted endorsement of violence to protect the national ingroup, which in turn predicted a willingness to die for the group. These statistical models accounted for an average of 31.4% of the variance in willingness to die for the group, after accounting for demographic variables. Furthermore, cognitive inflexibility was related to greater confidence in the decision to sacrifice one’s life in an ingroup trolley problem scenario. Analysis of participants’ performance on the cognitive tasks revealed that cognitive rigidity – distinctly from other aspects of cognition – was specifically implicated as a cognitive antecedent of extremist attitudes. Implications for the study of radicalization and identity fusion throug... (shrink)

Vacuum radiation causes a particle to make a random walk about its dynamical trajectory. In this random walk the root mean square change in spatial coordinate is proportional to t 1/2, and the fractional changes in momentum and energy are proportional to t −1/2, where t is time. Thus the exchange of energy and momentum between a particle and the vacuum tends to zero over time. At the end of a mean free path the fractional change in momentum of (...) a particle in a gas is very small. However, at the end of the mean free path each particle undergoes an interaction that magnifies the preceding change, and the net result is that the momentum distribution of the particles in a gas is randomized in a few collision times. In this way the random action of vacuum radiation and its subsequent magnification by molecular interaction produces entropy increase. This process justifies the assumption of molecular chaos used in the Boltzmann transport equation. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Forms of Life and Cultural EndowmentsVictor Peterson IIYou know, honey, us colored folk is branches without roots and that makes things come round in queer ways.—Zora Neale Hurston (Their Eyes Were Watching God 15)what does it mean when we speak of a form of life? When speaking of a form of life, we consider one different from others by way of its mode of expression, that is, by its (...) means of construction. This interpretation lends itself to a functional analysis of the material put to use and whose operations jointly express the concept we are after. Modes of expression can be plotted between a rhetorical and semantic axis (Gates 48). As such, "[t]he level of connotation of the visual sign, of its contextual reference and positioning in different discursive fields of meaning and association, is the point where already coded signs intersect with the deep semantic codes of a culture and take on additional more active ideological dimensions" (Hall 56). Coordinates within this domain encode signifying practices, revitalizing the traditional concept of signification as a function of what's signified with respect to a signifier. The content of a syntagm in this coordinate system, a point in this plane, indexes its function with respect to others. As such, we will conceive of the content of modes of expression functionally.A function is defined by pairing an element from a domain and another from a sub/co-domain whereby that pair is an element of that function. In this way, we can treat functions as abstract objects. If we treat a domain as what determines the availability of an expression, and a sub/co-domain as representative of its range of application, then the function of applying some proposition maps a movement from a domain of selection to one of composition, that is, its use with respect to others. The function of an expression, then, represents an operation over the possible worlds of its appropriate application (Taylor 201–02, 269, 276). This becomes more interesting when considering assertions whereby one subject is known to be the case for another, a concept that's modeled when a proposition from one is appearing in the object position of another (Fara 65–73). Resultingly, a proposal for an [End Page 26] ontology constituted by modes of interaction rather than identity stipulations to physical entities arises. It follows that if a form of life is understood by way of its mode of expression, then its content is expressed as an ensemble of the functions of its operations. Let this ensemble of functions be called an endowment.There is a pervasive debate in cultural studies that obsesses over proprietary notions as well as the ability to locate an origin. With that in mind, let us consider a coordinate system where there are two perpendicular axes, and we define positions within the space provided at the intersection of lines drawn from each. Each axis is represented by an ordered series of markers. A line drawn from each axis indicates that the coordinates indexed at their intersection is a function of these two markers. This locates an individual at a point in that domain, indexing a relation between the axes framing that space. Therefore, that coordinate-wise space, here a domain of possible expression, is not "empty" as pessimists would claim, but is filled with functional-content, albeit functions yet applied and marked by a point in that plane.Although we are currently speaking of two-dimensional space, the same follows for as many dimensions as we want. A point's location is a function of three values in three dimensions, four in four dimensions, and so on. Forms of life, then, will be comprised of four dimensions. This allows for a space-time conception, wherein joint expressions bend space-time and that space dictates those individuals' possible movements. From this, we construct a geometrical model of space-time represented as a cube composed of two-dimensional slices with these slices extending in a particular direction like cards stacked one on top of the other to model time.We want our conception of a form of life to be spatial. After all, it... (shrink)

Every year, millions of students in the United States and around the world graduate from high school and college. Commencement speakers—often distilling the hopes of parents and four years of messaging from educators—tell graduates that they must do something grand, ambitious, or far-reaching. Change the world. Disrupt the status quo. Every problem in the world is your problem, awaiting your solutions. -/- This book is an antidote to that advice. It provides a clear-eyed assessment of three types of people who (...) tend to believe and promote a commencement speaker’s view of the world: the moralizer, who imposes unnecessary social costs by inappropriately enforcing morality; the busybody, who thinks the stranger and close friend merit equal shares of our benevolent attention; and the pure hearted, who equates acting with good intentions with just outcomes. The book also provides a bold defense of living an ordinary life by putting down roots, creating a good home, and living in solitude. A quiet, peaceful life can be generous and noble. It’s OK to mind your own business. (shrink)

Beyond being the first substantial publication on Fourier, this work contains the text of Fourier's seminal paper of 1807 on the propagation of heat, marking the first time it has ever appeared in print. This paper incorporates many of the mathematical creations on which Fourier's fame rests, including derivation of the diffusion equation, the separation of the treatment of surface phenomena from internal phenomena, the use of boundary values and initial conditions, and the development of "Fourier series" and the so-called (...) "Bessel functions."When submitted to the examiners of the Institut de France, the originality of the paper and the surprising nature of some of its mathematical revelations caused great controversy, and it was denied publication both in 1807 and in later years. Fourier had the support, among the examiners, of Laplace and Monge, but Lagrange was adamantly in opposition, so that Fourier's work did not appear in print until 1822, reworked into book form.Fourier's mathematical discoveries are intimately related to his interest in the solution of physical problems and their experimental verification. The mathematical methods he developed in connection with heat diffusion apply to physical situations far beyond the boundaries of this area. Generally, Fourier may be credited with one of the first major extensions of mathematical physics beyond the applications of Newton's laws of motion and universal gravitation.The opening biographical chapter of this book follows Fourier's career up to the submission of the 1807 paper, and the two closing chapters take up his life and work from that point on. Fourier had strong political motivations and spent much of his life in the public service. These chapters trace his political difficulties, both before and after 1807, when he was the prefect of a department of France and was subjected to the dislocations of Napoleon's ups and downs. These chapters also describe aspects of the turbulent but productive development of French science from the Revolution to 1830.The core of the book presents the paper of 1807 in its original French and with the original notation. Grattan-Guinness has divided the paper into sections by the sequence of the problems taken up, and he introduces and, where necessary, closes each section with commentary relevant to Fourier's later work in these areas. The paper itself (cllows the chronology of Fourier's discoveries, and among the topics treated are, in this order: heat diffusion between disjoint bodies and in continuous bodies; the appearance of partial differential equations; the special solution for the lamina; sine and cosine series for an arbitrary function; reflections on the vibrating string problem; solution for the annulus; the full Fourier series for an arbitrary function; reflections on n-body analysis; solution for the sphere; solution for the cylinder; steady-state diffusion in the rectangular prism; time-dependent diffusion in the cube; and Fourier's experimental work. (shrink)

Mind, it has recently been argued1, is a thoroughly temporal phenomenon: so temporal, indeed, as to defy description and analysis using the traditional computational tools of cognitive scientific understanding. The proper explanatory tools, so the suggestion goes, are instead the geometric constructs and differential equations of Dynamical Systems Theory. I consider various aspects of the putative temporal challenge to computational understanding, and show that the root problem turns on the presence of a certain kind of causal web: a (...) web that involves multiple components (both inner and outer) linked by chains of continuous and reciprocal causal influence. There is, however, no compelling route from such facts about causal and temporal complexity to the radical anti- computationalist conclusion. This is because, interactive complexities notwithstanding, the computational approach provides a kind of explanatory understanding that cannot (I suggest) be recreated using the alternative resources of pure Dynamical Systems Theory. In particular, it provides a means of mapping information flow onto causal structure -- a mapping that is crucial to understanding the distinctive kinds of flexibility and control characteristic of truly mindful engagements with the world. Where we confront especially complex interactive causal webs, however, it does indeed become harder to isolate the syntactic vehicles required by the computational approach. Dynamical Systems Theory, I conclude, may play a vital role in recovering such vehicles from the burgeoning mass of real-time interactive complexity. (shrink)

This paper suggests a new approach (with old roots) to the study of the connection between logic and geometry. Traditionally, most logic diagrams associate only vertices of shapes with propositions. The new approach, which can be dubbed ’full logical geometry’, aims to associate every element of a shape (edges, faces, etc.) with a proposition. The roots of this approach can be found in the works of Carroll, Jacoby, and more recently, Dubois and Prade. However, its potential has not been duly (...) appreciated, probably because of the complexity of the diagrams in these works. The following study demonstrates how the Hexagon of Opposition can be represented as a triangle and Classical Logic as a tetrahedron (rather than a rhombic dodecahedron). It then applies the approach to modal logic, extending the tetrahedron for the logic KT into a dipyramid and a cube for KD, and finally an octahedron for K. Some possible directions for further research are also indicated. (shrink)

We introduce new proof systems G[β] and G ext[β], which are equivalent to the standard equational calculi of λβ- and λβη- conversion, and which may be qualified as ‘analytic’ because it is possible to establish, by purely proof-theoretical methods, that in both of them the transitivity rule admits effective elimination. This key feature, besides its intrinsic conceptual significance, turns out to provide a common logical background to new and comparatively simple demonstrations—rooted in nice proof-theoretical properties of transitivity-free derivations—of a number (...) of well-known and central results concerning β- and βη-reduction. The latter include the Church–Rosser theorem for both reductions, the Standardization theorem for β- reduction, as well as the Normalization (Leftmost reduction) theorem and the Postponement of η-reduction theorem for βη-reduction. (shrink)

Recent work on the history of General Relativity by Renn, Sauer, Janssen et al. shows that Einstein found his field equations partly by a physical strategy including the Newtonian limit, the electromagnetic analogy, and energy conservation. Such themes are similar to those later used by particle physicists. How do Einstein's physical strategy and the particle physics derivations compare? What energy-momentum complex did he use and why? Did Einstein tie conservation to symmetries, and if so, to which? How did his (...) work relate to emerging knowledge of the canonical energy-momentum tensor and its translation-induced conservation? After initially using energy-momentum tensors hand-crafted from the gravitational field equations, Einstein used an identity from his assumed linear coordinate covariance x'=Mx to relate it to the canonical tensor. Usually he avoided using matter Euler-Lagrange equations and so was not well positioned to use or reinvent the Herglotz-Mie-Born understanding that the canonical tensor was conserved due to translation symmetries, a result with roots in Lagrange, Hamilton and Jacobi. Whereas Mie and Born were concerned about the canonical tensor's asymmetry, Einstein did not need to worry because his Entwurf Lagrangian is modeled not so much on Maxwell's theory as on a scalar theory. Einstein's theory thus has a symmetric canonical energy-momentum tensor. But as a result, it also has 3 negative-energy field degrees of freedom. Thus the Entwurf theory fails a 1920s-30s a priori particle physics stability test with antecedents in Lagrange's and Dirichlet's stability work; one might anticipate possible gravitational instability. This critique of the Entwurf theory can be compared with Einstein's 1915 critique of his Entwurf theory for not admitting rotating coordinates and not getting Mercury's perihelion right. One can live with absolute rotation but cannot live with instability. Particle physics also can be useful in the historiography of gravity and space-time, both in assessing the growth of objective knowledge and in suggesting novel lines of inquiry to see whether and how Einstein faced the substantially mathematical issues later encountered in particle physics. This topic can be a useful case study in the history of science on recently reconsidered questions of presentism, whiggism and the like. Future work will show how the history of General Relativity, especially Noether's work, sheds light on particle physics. (shrink)

In the 1687 Principia, Newton gave a solution to the direct problem (given the orbit and center of force, find the central force) for a conic-section with a focal center of force (answer: a reciprocal square force) and for a spiral orbit with a polar center of force (answer: a reciprocal cube force). He did not, however, give solutions for the two corresponding inverse problems (given the force and center of force, find the orbit). He gave a cryptic solution (...) to the inverse problem of a reciprocal cube force, but offered no solution for the reciprocal square force. Some take this omission as an indication that Newton could not solve the reciprocal square, for, they ask, why else would he not select this important problem? Others claim that ``it is child's play'' for him, as evidenced by his 1671 catalogue of quadratures (tables of integrals). The answer to that question is obscured for all who attempt to work through Newton's published solution of the reciprocal cube force because it is done in the synthetic geometric style of the 1687 Principia rather than in the analytic algebraic style that Newton employed until 1671. In response to a request from David Gregory in 1694, however, Newton produced an analytic version of the body of the proof, but one which still had a geometric conclusion. Newton's charge is to find both ``the orbit'' and ``the time in orbit.'' In the determination of the dependence of the time on orbital position, t(r), Newton evaluated an integral of the form ∫dx/xn to calculate a finite algebraic equation for the area swept out as a function of the radius, but he did not write out the analytic expression for time t = t(r), even though he knew that the time t is proportional to that area. In the determination of the orbit, θ (r), Newton obtained an integral of the form ∫dx/√(1−x2) for the area that is proportional to the angle θ, an integral he had shown in his 1669 On Analysis by Infinite Equations to be equal to the arcsin(x). Since the solution must therefore contain a transcendental function, he knew that a finite algebraic solution for θ=θ(r) did not exist for ``the orbit'' as it had for ``the time in orbit.'' In contrast to these two solutions for the inverse cube force, however, it is not possible in the inverse square solution to generate a finite algebraic expression for either ``the orbit'' or ``the time in orbit.'' In fact, in Lemma 28, Newton offers a demonstration that the area of an ellipse cannot be given by a finite equation. I claim that the limitation of Lemma 28 forces Newton to reject the inverse square force as an example and to choose instead the reciprocal cube force as his example in Proposition 41. (shrink)

We use Bub's (2016) correlation arrays and Pitowksy's (1989b) correlation polytopes to analyze an experimental setup due to Mermin (1981) for measurements on the singlet state of a pair of spin-12 particles. The class of correlations allowed by quantum mechanics in this setup is represented by an elliptope inscribed in a non-signaling cube. The class of correlations allowed by local hidden-variable theories is represented by a tetrahedron inscribed in this elliptope. We extend this analysis to pairs of particles of (...) arbitrary spin. The class of correlations allowed by quantum mechanics is still represented by the elliptope; the subclass of those allowed by local hidden-variable theories by polyhedra with increasing numbers of vertices and facets that get closer and closer to the elliptope. We use these results to advocate for an interpretation of quantum mechanics like Bub's. Probabilities and expectation values are primary in this interpretation. They are determined by inner products of vectors in Hilbert space. Such vectors do not themselves represent what is real in the quantum world. They encode families of probability distributions over values of different sets of observables. As in classical theory, these values ultimately represent what is real in the quantum world. Hilbert space puts constraints on possible combinations of such values, just as Minkowski space-time puts constraints on possible spatio-temporal constellations of events. Illustrating how generic such constraints are, the equation for the elliptope derived in this paper is a general constraint on correlation coefficients that can be found in older literature on statistics and probability theory. Yule (1896) already stated the constraint. De Finetti (1937) already gave it a geometrical interpretation. (shrink)

Scientists have used models for hundreds of years as a means of describing phenomena and as a basis for further analogy. In Scientific Models in Philosophy of Science, Daniela Bailer-Jones assembles an original and comprehensive philosophical analysis of how models have been used and interpreted in both historical and contemporary contexts. Bailer-Jones delineates the many forms models can take (ranging from equations to animals; from physical objects to theoretical constructs), and how they are put to use. She examines early (...) mechanical models employed by nineteenth-century physicists such as Kelvin and Maxwell, describes their roots in the mathematical principles of Newton and others, and compares them to contemporary mechanistic approaches. Bailer-Jones then views the use of analogy in the late nineteenth century as a means of understanding models and to link different branches of science. She reveals how analogies can also be models themselves, or can help to create them. The first half of the twentieth century saw little mention of models in the literature of logical empiricism. Focusing primarily on theory, logical empiricists believed that models were of temporary importance, flawed, and awaiting correction. The later contesting of logical empiricism, particularly the hypothetico-deductive account of theories, by philosophers such as Mary Hesse, sparked a renewed interest in the importance of models during the 1950s that continues to this day. Bailer-Jones analyzes subsequent propositions of: models as metaphors; Kuhn's concept of a paradigm; the Semantic View of theories; and the case study approaches of Cartwright and Morrison, among others. She then engages current debates on topics such as phenomena versus data, the distinctions between models and theories, the concepts of representation and realism, and the discerning of falsities in models. (shrink)

A previously unexplored method, combining logical and mathematical elements, is shown to yield substantial numerical improvements in the area of Diophantine approximations. Kreisel illustrated the method abstractly by noting that effective bounds on the number of elements are ensured if Herbrand terms from ineffective proofs of Σ 2 -finiteness theorems satisfy certain simple growth conditions. Here several efficient growth conditions for the same purpose are presented that are actually satisfied in practice, in particular, by the proofs of Roth's theorem due (...) to Roth himself and to Esnault and Viehweg. The analysis of the former yields an exponential bound of order exp(70ε -2 d 2 ) in place of exp(285ε -2 d 2 ) given by Davenport and Roth in 1955, where α is (real) algebraic of degree d ≥ 2 and $|\alpha - pq^{-1}| . (Thus the new bound is less than the fourth root of the old one.) The new bounds extracted from the other proof are polynomial of low degree (in ε -1 and log d). Corollaries: Apart from a new bound for the number of solutions of the corresponding Diophantine equations and inequalities (among them Thue's inequality), $\log \log q_\nu , where q ν are the denominators of the convergents to the continued fraction of α. (shrink)

This paper proposes an approach to investigate norm-governed learning agents which combines a logic-based formalism with an equation-based counterpart. This dual formalism enables us to describe the reasoning of such agents and their interactions using argumentation, and, at the same time, to capture systemic features using equations. The approach is applied to norm emergence and internalisation in systems of learning agents. The logical formalism is rooted into a probabilistic defeasible logic instantiating Dung’s argumentation framework. Rules of this logic are (...) attached with probabilities to describe the agents’ minds and behaviours as well as uncertain environments. Then, the equation-based model for reinforcement learning, defined over this probability distribution, allows agents to adapt to their environment and self-organise. (shrink)

In Cardano’s classification in the Ars Magna, the cubic equations were arranged in thirteen families. This paper examines the well-known solution methods for the families $$x^3 + a_1x = a_0$$ x 3 + a 1 x = a 0 and $$x^3 = a_1x + a_0$$ x 3 = a 1 x + a 0 and then considers thoroughly the systematic interconnections between these two families and the remaining ones and provides a diagram to visualize the results clearly. In the (...) analysis of these solution methods, we pay particular attention to the appearance of the square roots of negative numbers even when all the solutions are real—the so-called casus irreducibilis. The structure that comes to light enables us to fully appreciate the impact that the difficulty entailed by the casus irreducibilis had on Cardano’s construction in the Ars Magna. Cardano tried to patch matters first in the Ars Magna itself and then in the De Regula Aliza. We sketch the former briefly and analyze the latter in detail because Cardano considered it the ultimate solution. In particular, we examine one widespread technique that is based on what I have called splittings. (shrink)

Christopher Rowe's new book is an ambitious attempt to walk the tightrope between, on the one hand, bone-headed neglect of Plato's use of dramatic form, and, on the other, obtuse blindness to the presence of a serious philosophical agenda. This locates Rowe on the cutting edge of current methodological controversies, but his book also has deep roots in the past. He harks back to the oft-maligned Paul Shorey to offer an updated, newly sophisticated "unitarian" reading of the dialogues, one that (...) depends heavily on equating Plato's own voice with that of his Socrates, who serves as "[Plato's] alter ego, his persona, his mask". This Socrates is not merely a mouthpiece for a developing Plato's changing views, but a coherent character who represents a consistent Platonic voice throughout the works in which he appears—and even those in which he doesn't. Among other things, this close identification of Plato with Socrates requires Rowe to apply the principle of charity not just to the author, but to his creation. Since Plato and Socrates are one, Plato is fully accountable for all the arguments he assigns to Socrates: there is no dramatic wiggle-room for him to assign the latter any truly bad arguments for his own authorial purposes. (shrink)

Before examining de Moivre's contributions to the science of mathematics, this article reviews the source materials, consisting of the printed works and the correspondence of de Moivre, and constructs his biography from them. The analytical part examines de Moivre's contributions and achievements in the study of equations, series, and the calculus of probability. De Moivre contributed to the continuing development from Viète to Abel and Galois of the theory of solving equations by means of constructing particular equations, (...) the roots of which can be written in the form $$\sqrt[n]{{a + \sqrt b }} + \sqrt[n]{{a - \sqrt b }}$$. He also discovered the reciprocal equations. In the course of this work de Moivre discovered an expression equivalent to (cos α+i sin α) n =cos n α+i sin n α and, following Cotes, he succeeded in expressing the nth roots of unity in trigonometric form. In the theory of series, de Moivre developed a polynomial theorem encom-passing Newton's binomial theorem and, in particular, a theorem of recurrent series useful in the calculus of probability. The demands of the calculus of probability led de Moivre to an approximation for the binomial coefficients $$\left( {_m^n } \right)$$ for large values of n. The interaction between de Moivre and James Stirling, particularly in regard to the asymptotic series for log (n!), is treated at length. This work supplied the foundation for de Moivre's limit theorem for the binomial distribution. The calculus of probability, which occupied him from 1708 onward, became in time ever more the center of de Moivre's inquiries. Proceeding from contemporary collections of gambling exercises, de Moivre, by introducing an explicit measure of probability for the so-called Laplace experiments, found the beginnings of a theory of probability. De Moivre expanded the classic application of probability calculus to games of chance by addressing himself to the problem of annuities and by adopting Halley's work with its conception of “Probability of life”. De Moivre was the first to publish a mathematically formulated law for the decrements of life derived from mortality tables. (shrink)

Religious moderation has been popular and widely promoted to students as a countermeasure to radicalism. However, it runs across several challenges. Not to mention that radicalism has extended its influence within Islamic universities in Indonesia. Many research organisations have found that Indonesian students tend to be radical. Hence, the discussion around religious moderation among students highlights its urgency. With emphasis on the reception of Islamic university students to religious texts, this study proposed the appropriate approach to religious moderation in the (...) context of plural Indonesian society with the reception of Qur’anic verses and hadiths that promoted moderation. It employed a qualitative approach with a purposive sampling technique involving 81 students of Islamic Religious Education of UIN Maulana Malik Ibrahim Malang as the research subjects. They were students from four semester IV and VI classes. This study revealed several key findings: firstly, the majority of students equate religious moderation with religious tolerance; secondly, students draw from a range of verses and hadiths that emphasise religious moderation, primarily on tolerance promotion; and thirdly, students’ application of religious moderation based on religious texts manifests through verbal, written and practical approaches. This study presents a model for developing religious moderation rooted in students’ comprehension of religious texts advocating moderation. This study implies using religious texts to promote moderate thought to lessen radicalism and intolerance in the world. Contribution: This study introduces a religious text-oriented approach to enhance the development of religious moderation, thereby refining strategies and methods that have predominantly emphasised aspects of social reality. The religious texts that advocate for moderation are accepted and applied by students in their lives. This contribution is crucial to lessening radicalism and intolerance in Indonesia. (shrink)

Author cultivated fermenting cells (Scccharomyces spec.) in must of grapes and measured the various vital phenomena. The data thus received described in a rectangular co-ordinate as a function of time, found three kinds of characteristic curves in every vital phenomenon (whether belonging to the group of feeding, growth or that of increase): I. the curve described bySachs in 1873 and called the curve of the great period of evolution (Fig. 1:s). 2. the one described byM. G. Harting in 1845, and (...) the curve of individual or ontogenetic evolution (Fig. 1:S). 3. the undulatory curve similar to a sinus-cosinus function, deduced in theory by author and later on, in 1915, also found on an experimental basis (Fig. 3). — Analysing these curves, author demonstrates that they are in the closest relationship with each other. The course ofSachs' great period is identical with the function of the aperiodically mitigated vibromotion; the course ofHarting's ontogenetic curve is identical with the integral of the previous aperiodic function; the undulatory curve discovered by the author, and the one belonging to the philogenesis of evolution, consist of two details, one of the members is formed from the function of aperiodically mitigated vibromotion, and the other from a function of periodically mitigated vibration. — Mitigated vibromotion, according to our present knowledge can only arise if a body capable of vibration is simultaneously affected by a force establishing movement and a resistance mitigating the movement. In the living organism, on this basis, there is also a force and a resistance. The living organism obtains this force from food while the resistance is rooted in the construction of the cell. The author proves that the cells which no longer divide (the so-called permanent tissueforming cells) follow an aperiodical vibromotor course in their development while in the development of the continually dividing, so-called meristematic cells, owing to the periodic change of division and regeneration, the potential of the energy accommodates itself to the periodic vibromotor course. Both forms of development are derived from the identical differential equation: d2s/dt2=−w2s−2r ds/dt, the only difference between the two phenomena is that by aperiodic oscillation it is r2>w2 while by periodic it is r2equations, the constants changing according to the biological conditions, and that we can accurately follow the course of the phenomena with the method of theoretic physics and furthermore, that we have found the connection between these two chapters of evolution. (shrink)