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  Beyond Wavefunctions: A Time-Symmetric Nonlocal Ontology for Quantum Mechanics

  Yakir Aharonov, Eliahu Cohen, and Avshalom C. Elitzur

  "We take Agassi's attitude to QM as an invitation to present some insights we have gained during our research in this field. Following is a highly non-technical account of a few works which we believe begins to merge into a novel and rich picture of physical reality."

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  Forcing Optimality and Brandt's Principle

  Domenico Napoletani, Marco Panza, and Daniele C. Struppa

  We argue that many optimization methods can be viewed as representatives of “forcing”, a methodological approach that attempts to bridge the gap between data and mathematics on the basis of an a priori trust in the power of a mathematical technique, even when detailed, credible models of a phenomenon are lacking or do not justify the use of this technique. In particular, we show that forcing is implied in particle swarms optimization methods, and in modeling image processing problems through optimization. From these considerations, we extrapolate a principle for general data analysis methods, what we call ‘Brandt’s principle’, namely the assumption that an algorithm that approaches a steady state in its output has found a solution to a problem, or needs to be replaced. We finally propose that biological systems, and other phenomena that respect general rules of morphogenesis, are a natural setting for the application of this principle

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  Euler’s Introductio in analysin infinitorum and the Program of Algebraic Analysis: Quantities, Functions and Numerical Partitions

  Marco Panza

  After discussing in general Euler's program of algebraic analysis, as it is presented in the Introductio (1748), two particular topics are taken into account: Euler's notion of function and his analytic theory of numerical partitions.

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  On Benacerraf’s Dilemma, Again

  Marco Panza

  In spite of its enormous influence, Benacerraf’s dilemma admits no standard unanimously accepted formulation. This mainly depends on Benacerraf’s having originally presented it in a quite colloquial way, by avoiding any compact, somehow codified, but purportedly comprehensive formulation (Benacerraf 1973 cf. p. 29).

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  Bernstein-type Inequalities for Bicomplex Polynomials

  Irene Sabadini, Adrian Vajiac, and Mihaela Vajiac

  This paper considers the well-known Bernstein and Erdős–Lax inequalities in the case of bicomplex polynomials. We shall prove that the validity of these inequalities depends on the norm in use and we consider the cases of the Euclidean, Lie, dual Lie and hyperbolic-valued norms. In particular, we show that in the case of the Euclidean norm the inequalities holds keeping the same relation with the degree of the polynomial that holds in the classical complex case, but we have to enlarge the radius of the ball. In the case of the dual Lie norm both the relation with the degree and the radius of the ball have to be changed. Finally, we prove that the exact analogs of the two inequalities hold when considering the Lie norm and the hyperbolic-valued norm. In the case of these two norms we also show the validity of the maximum modulus principle for bicomplex holomorphic functions.

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  A Complex Analysis Problem Book (Second Edition)

  Daniel Alpay

  This second edition presents a collection of exercises on the theory of analytic functions, including completed and detailed solutions. It introduces students to various applications and aspects of the theory of analytic functions not always touched on in a first course, while also addressing topics of interest to electrical engineering students (e.g., the realization of rational functions and its connections to the theory of linear systems and state space representations of such systems). It provides examples of important Hilbert spaces of analytic functions (in particular the Hardy space and the Fock space), and also includes a section reviewing essential aspects of topology, functional analysis and Lebesgue integration.

  Benefits of the 2nd edition

  Rational functions are now covered in a separate chapter. Further, the section on conformal mappings has been expanded.

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  An Introduction to Superoscillatory Sequences

  Fabrizio Colombo, Irene Sabadini, and Daniele C. Struppa

  The notion of superoscillating functions, or more properly of superoscillatory sequences, is a byproduct of Aharonov's theory of weak measurements and weak values in quantum mechanics. Recently, many mathematicians and physicists have begun to pay attention to the mathematical significance of such objects, and have been able to begin a theory of superoscillatory behavior. Not surprisingly, this theory is based on some classical results in Fourier analysis, and it displays interesting connections with the theory of convolution equations. In this paper we will put these connections in a larger context, and show how to use this context to generate a large class of superoscillating sequences. As a concrete example we discuss the Cauchy problem with superoscillatory datum for the harmonic oscillator. Finally, we show how this theory can be generalized to the case of several variables.

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  Flipped Classroom Model: Effects on Performance, Attitudes and Perceptions in High School Algebra

  Peter Esperanza, Khristin Fabian, and Criselda Toto

  In this study, we evaluated student perceptions of the flipped classroom model and its effects to students’ performance and attitudes to mathematics. A randomized controlled trial with 91 high school algebra students was conducted. The experimental group participated in a year-long intervention of the flipped classroom model while the control group followed the traditional lesson delivery. Results of the year-end evaluation of this model showed positive student perceptions. An analysis of covariance of the algebra post-test score with learning model as treatment factor and pre-test as covariate resulted in a significant treatment effect at .05 level of significance. A paired-sample t-test by treatment group to compare pre-test and post-test math attitude scores resulted in a significant decrease in the control groups’ value of mathematics while the experimental group had a significant positive change in their confidence and enjoyment of mathematics.

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  Mathematics Is Physics

  Matthew S. Leifer

  In this essay, I argue that mathematics is a natural science---just like physics, chemistry, or biology---and that this can explain the alleged "unreasonable" effectiveness of mathematics in the physical sciences. The main challenge for this view is to explain how mathematical theories can become increasingly abstract and develop their own internal structure, whilst still maintaining an appropriate empirical tether that can explain their later use in physics. In order to address this, I offer a theory of mathematical theory-building based on the idea that human knowledge has the structure of a scale-free network and that abstract mathematical theories arise from a repeated process of replacing strong analogies with new hubs in this network. This allows mathematics to be seen as the study of regularities, within regularities, within ..., within regularities of the natural world. Since mathematical theories are derived from the natural world, albeit at a much higher level of abstraction than most other scientific theories, it should come as no surprise that they so often show up in physics.

  This version of the essay contains an addendum responding to Slyvia Wenmackers' essay and comments that were made on the FQXi website.

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  Abstraction and Epistemic Economy

  Marco Panza

  Most of the arguments usually appealed to in order to support the view that some abstraction principles are analytic depend on ascribing to them some sort of existential parsimony or ontological neutrality, whereas the opposite arguments, aiming to deny this view, contend this ascription. As a result, other virtues that these principles might have are often overlooked. Among them, there is an epistemic virtue which I take these principles to have, when regarded in the appropriate settings, and which I suggest to call ‘epistemic economy’. My purpose is to isolate and clarify this notion by appealing to some examples concerning the definition of natural and real numbers.

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  An Advanced Complex Analysis Problem Book: Topological Vector Spaces, Functional Analysis, and Hilbert Spaces of Analytic Functions

  Daniel Alpay

  This is an exercises book at the beginning graduate level, whose aim is to illustrate some of the connections between functional analysis and the theory of functions of one variable. A key role is played by the notions of positive definite kernel and of reproducing kernel Hilbert space. A number of facts from functional analysis and topological vector spaces are surveyed. Then, various Hilbert spaces of analytic functions are studied.

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  Preface to "Intertwingled: The Work and Influence of Ted Nelson"

  Douglas R. Dechow and Daniele C. Struppa

  This is the preface to "Intertwingled: The Work and Influence of Ted Nelson", which examines and honors the work and influence of the computer visionary and re-imagines its meaning for the future. Emerging from a conference held in 2014 at Chapman University, it includes contributions from world-renowned computer scientists and media figures.

  The full text of this book is available on an open access basis at Springer.

  The blog for the Intertwingled Conference can be read here.

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  "It from Bit" and the Quantum Probability Rule

  Matthew S. Leifer

  I argue that, on the subjective Bayesian interpretation of probability, "it from bit" requires a generalization of probability theory. This does not get us all the way to the quantum probability rule because an extra constraint, known as noncontextuality, is required. I outline the prospects for a derivation of noncontextuality within this approach and argue that it requires a realist approach to physics, or "bit from it". I then explain why this does not conflict with "it from bit". This version of the essay includes an addendum responding to the open discussion that occurred on the FQXi website. It is otherwise identical to the version submitted to the contest.

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  Newton on Indivisibles

  Antoni Malet and Marco Panza

  Though Wallis’s Arithmetica infinitorum was one of Newton’s major sources of inspiration during the first years of his mathematical education, indivisibles were not a central feature of his mathematical production.

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  Wallis on Indivisibles

  Antoni Malet and Marco Panza

  The present chapter is devoted, first, to discuss in detail the structure and results of Wallis’s major and most influential mathematical work, the Arithmetica Infinitorum (Wallis 1656). Next we will revise Wallis’s views on indivisibles as articulated in his answer to Hobbes’s criticism in the early 1670s. Finally, we will turn to his discussion of the proper way to understand the angle of contingence in the first half of the 1680s. As we shall see, there are marked differences in the status that indivisibles seem to enjoy in Wallis’s thought along his mathematical career. These differences correlate with the changing context of seventeenth century mathematics from the 1650s through the 1680s, but also respond to the different uses Wallis gave to indivisibles in different kinds of texts—purely mathematical, openly polemical, or devoted to philosophical discussion of foundational matters.

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  «“Una stessa cosa”». Come intendere la definizione della continuità di Aristiotele

  Marco Panza

  I focus on the definition of continuity Aristotle advances in Physics V.3 and contrast two different possible interpretations if it, by suggesting that one if them is more appropriate.

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  Introduction to Functions and Generality of Logic. Reflections on Frege's and Dedekind's Logicisms

  Hourya Benis Sinaceur, Marco Panza, and Gabriel Sandu

  This book examines three connected aspects of Frege’s logicism: the differences between Dedekind’s and Frege’s interpretation of the term ‘logic’ and related terms and reflects on Frege’s notion of function, comparing its understanding and the role it played in Frege’s and Lagrange’s foundational programs. It concludes with an examination of the notion of arbitrary function, taking into account Frege’s, Ramsey’s and Russell’s view on the subject. Composed of three chapters, this book sheds light on important aspects of Dedekind’s and Frege’s logicisms. The first chapter explains how, although he shares Frege’s aim at substituting logical standards of rigor to intuitive imports from spatio-temporal experience into the deductive presentation of arithmetic, Dedekind had a different goal and used or invented different tools. The chapter highlights basic dissimilarities between Dedekind’s and Frege’s actual ways of doing and thinking. The second chapter reflects on Frege’s notion of a function, in comparison with the notions endorsed by Lagrange and the followers of the program of arithmetization of analysis. It remarks that the foundational programs pursued by Lagrange and Frege are crucially different and based on a different idea of what the foundations of mathematics should be like. However, despite this contrast, the notion of function plays similar roles in the two programs, and this chapter emphasizes the similarities. The third chapter traces the development of thinking about Frege’s program in the foundations of mathematics, and includes comparisons of Frege’s, Russell’s and Ramsey’s views. The chapter discusses earlier papers written by Hintikka, Sandu, Demopoulos and Trueman. Although the chapter’s main focus is on the notion of arbitrary correlation, it starts out by discussing some aspects of the connection between this notion and Dedekind Theorem.

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  Generalized Quaternionic Schur Functions in the Ball and Half-Space and Krein-Langer Factorization

  Daniel Alpay, Fabrizio Colombo, and Irene Sabadini

  In this paper we prove a new version of Krein-Langer factorization theorem in the slice hyperholomorphic setting which is more general than the one proved in [8]. We treat both the case of functions with κ negative squares defined on subsets of the quaternionic unit ball or on subsets of the half space of quaternions with positive real part. A crucial tool in the proof of our results is the Schauder-Tychonoff theorem and an invariant subspace theorem for contractions in a Pontryagin space.

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  The Fock Space in the Slice Hyperholomorphic Setting

  Daniel Alpay, Fabrizio Colombo, Irene Sabadini, and Guy Salomon

  In this paper we introduce and study some basic properties of the Fock space (also known as Segal-Bargmann space) in the slice hyperholomorphic setting. We discuss both the case of slice regular functions over quaternions and also the case of slice monogenic functions with values in a Clifford algebra. In the specific setting of quaternions, we also introduce the full Fock space. This paper can be seen as the beginning of the study of infinite dimensional analysis in the quaternionic setting.

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  Basics of Functional Analysis with Bicomplex Scalars, and Bicomplex Schur Analysis

  Daniel Alpay, M. E. Luna-Elizarrarás, Michael Shapiro, and Daniele C. Struppa

  "With the goal of providing the foundations for a rigorous study of modules of bicomplex holomorphic functions, we develop here a general theory of functional analysis with bicomplex scalars."

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  Basics of Functional Analysis with Bicomplex Scalars, and Bicomplex Schur Analysis

  D. Alpay, M. E. Luna-Elizarrarás, M. Shapiro, and Daniele C. Struppa

  This book provides the foundations for a rigorous theory of functional analysis with bicomplex scalars. It begins with a detailed study of bicomplex and hyperbolic numbers and then defines the notion of bicomplex modules. After introducing a number of norms and inner products on such modules (some of which appear in this volume for the first time), the authors develop the theory of linear functionals and linear operators on bicomplex modules. All of this may serve for many different developments, just like the usual functional analysis with complex scalars and in this book it serves as the foundational material for the construction and study of a bicomplex version of the well known Schur analysis.

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  On the Indispensable Premises of the Indispensability Argument

  Andrea Sereni and Marco Panza

  We identify four different minimal versions of the indispensability argument, falling under four different varieties: an epistemic argument for semantic realism, an epistemic argument for platonism and a non-epistemic version of both. We argue that most current formulations of the argument can be reconstructed by building upon the suggested minimal versions. Part of our discussion relies on a clarification of the notion of (in)dispensability as relational in character. We then present some substantive consequences of our inquiry for the philosophical significance of the indispensability argument, the most relevant of which being that both naturalism and confirmational holism can be dispensed with, contrary to what is held by many.

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  Dust Storms and Their Influence on Atmospheric Parameters Over the Indo-Gangetic plains

  Ramesh P. Singh

  Dust storms are very common in the northern parts of India, and every year people living in the Indo-Gangetic plains suffer greatly. Dust storms affect day-to-day lives of people living in the Indo-Gangetic plains (IGP) and impact their health. The atmospheric and meteorological parameters are highly influenced by the dust storms and are found to affect the air quality that creates a big health threat and also affects the weather conditions. In this chapter, we discuss use of satellite remote sensing data in monitoring the dust events which occur every year during pre-monsoon season and their impacts on ocean, atmosphere, and meteorological parameters. Long-term effects of such dust storms on the climate of the northern parts of India are discussed. Such dust storms can be easily monitored using satellite data that can be used in issuing warning to the people so that they would not be exposed to such strong dust storms.

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  Using MapReduce Streaming for Distributed Life Simulation on the Cloud

  Atanas Radenski

  Distributed software simulations are indispensable in the study of large-scale life models but often require the use of technically complex lower-level distributed computing frameworks, such as MPI. We propose to overcome the complexity challenge by applying the emerging MapReduce (MR) model to distributed life simulations and by running such simulations on the cloud. Technically, we design optimized MR streaming algorithms for discrete and continuous versions of Conway’s life according to a general MR streaming pattern. We chose life because it is simple enough as a testbed for MR’s applicability to a-life simulations and general enough to make our results applicable to various lattice-based a-life models. We implement and empirically evaluate our algorithms’ performance on Amazon’s Elastic MR cloud. Our experiments demonstrate that a single MR optimization technique called strip partitioning can reduce the execution time of continuous life simulations by 64%. To the best of our knowledge, we are the first to propose and evaluate MR streaming algorithms for lattice-based simulations. Our algorithms can serve as prototypes in the development of novel MR simulation algorithms for large-scale lattice-based a-life models.

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  From Velocities to Fluxions

  Marco Panza

  "Though the De Methodis results, for its essential structure and content, from a re-elaboration of a previous unfinished treatise composed in the Fall of 1666—now known, after Whiteside, as The October 1666 tract on fluxions ([22], I, pp. 400-448)—, the introduction of the term ‘fluxion’ goes together with an important conceptual change concerned with Newton’s understanding of his own achievements. I shall argue that this change marks a crucial step in the origins of analysis, conceived as an autonomous mathematical theory."