Models are being used extensively for practicing and understanding scientific, engineering and mathematical subjects, but are rarely used as art analyzing tools, particularly, in learning environments. Contrarily, using art to explain mathematical ideas is not unprecedented. Strogatz (1988), for example, built a model based on Romeo and Juliet’s love story and used it to explain the idea of differential mathematics, and system dynamics. Artwork, specially written and plastic classics, is a fixed form of art. We frame them and put them (...) in a gallery, or a book (digital or physical). We don’t try to “fix” them or optimize their functioning, we analyze them to find meaning, intention, and patterns. In this article, we aim to show how, by building models combined with simple mathematical representations and analogies, it is possible to understand literary texts, from the prism of system and complexity theories, which emphasize the dynamic, non-linear, and non-reductionist aspects of the observed. We’ll demonstrate how modeling processes of three cultural assets, allow active correspondence with the original textual art, by treating them as systemic objects with interactions and dynamics. They will be analyzed while raising questions about the significance of modeling as a cognitive learning process. (shrink)

A review of Geoffrey B. Saxe, Cultural Development of Mathematical Ideas. Saxe offers a comprehensive treatment of social and linguistic change in the number systems used for economic exchange in the Oksapmin community of Papua New Guinea. By taking the cognition-is-social approach, Saxe positions himself within emerging perspectives that view cognition as enacted, situated, and extended. The approach is somewhat risky in that sociality surely does not exhaust cognition. Brains, bodies, and materiality also contribute to cognition—causally at least, (...) and possibly constitutively as well (as argued by Clark & Chalmers; Renfrew & Malafouris). This omission necessarily excludes the material dimension of numeracy. (shrink)

This paper aims to clarify Merleau-Ponty’s contribution to an embodied-enactive account of mathematical cognition. I first identify the main points of interest in the current discussions of embodied higher cognition and explain how they relate to Merleau-Ponty and his sources, in particular Husserl’s late works. Subsequently, I explain these convergences in greater detail by more specifically discussing the domains of geometry and algebra and by clarifying the role of gestalt psychology in Merleau-Ponty’s account. Beyond that, I explain how, for Merleau-Ponty, (...) mathematical cognition requires not only the presence and actual manipulation of some concrete perceptible symbols but, more strongly, how it is fundamentally linked to the structural transformation of the concrete configurations of symbolic systems to which these symbols appertain. Furthemore, I fill a gap in the literature by explaining Merleau-Ponty’s claim that these structural transformations are operated through motor intentionality. This makes it possible, in turn, to contrast Merleau-Ponty’s approach to ontologically idealistic and realistic views on mathematical objects. On Merleau-Ponty’s account, mathematical objects are relational entities, that is, gestalts that necessarily imply situated cognizers to whom they afford a specific type of engagement in the world and on whom they depend in their eventual structural transformations. I argue that, by attributing a strongly constitutive role to phenomenal configurations and their motor transformation in mathematical thinking, Merleau-Ponty contributes to clarifying the worldly, historical, and socio-cultural aspects of mathematical truths without compromising what we perceive as their universality, certainty, and necessity. (shrink)

Suppose one has a system, the infinite set of positive integers, P, and one wants to study the characteristics of a subset (or subsystem) of that system, the infinite subset of odd positives, O, relative to the overall system. In mathematics, this is done by pairing off each odd with a positive, using a function such as O=2P+1. This puts the odds in a one-to-one correspondence with the positives, thereby, showing that the subset of odds and the original set of (...) positives are the same size, or have the same cardinality. This counter-intuitive result ignores the “natural” relationship of one odd for every two positives in the sequence of positive integers, which would suggest that O is one-half the size of P. However, in the set of axioms that constitute mathematics, it is considered valid. Fair enough. In the physical universe (i.e., the starting system), though, relationships between entities matter. In biochemistry, if you start with an organism, say a rat, and you want to study its heart, you can do this by removing some heart cells and studying them in isolation in a cell culture system. But, the results often differ compared to what occurs in the intact animal because studying the isolated cultured cells ignores the relationships in the intact body between the cells, the rest of the heart tissue and the rest of the rat. In chemistry, if a copper atom were studied in isolation, it would never be known that copper atoms in bulk can conduct electricity because the atoms share their electrons. In physics, the relationships between inertial reference frames in relativity, and observer and observed in quantum physics can't be ignored. Relationships matter in the physical world, but the mathematics of infinite sets is still used to describe it. Does this matter? It seems to, at least in physics. Infinities cause numerous problems in theoretical physics such as non-renormalizability and problems in unifying quantum mehanics and general relativity . This suggests that the pairing off method and the mathematics of infinite sets based on it are analogous to a cell culture system or studying a copper atom in isolation if they are used in studying the physical universe because they ignore the inherent relationships between entities. In the real, physical world, the natural, inherent, relationships between entities can't be ignored. Said another way, the set of axioms that constitute abstract mathematics may be similar but not identical to the set of physical axioms by which the real, physical universe runs. This suggests that the results from abstract mathematics about infinities may not apply to or should be modified for use in physics. (shrink)

UNESCO Universal Declaration on Cultural Diversity (2 November 2001) defines culture with an emphasis on cultural features: “culture should be regarded as the set of distinctive spiritual, material, intellectual and emotional features of society or a social group”, encompassing, “in addition to art and literature, lifestyles, ways of living together, value systems, traditions and beliefs”. Cultural traits are also the primitive of mathematical models of cultural transmission inspired by population genetics, imported and refined by economics. (...) Any serious evaluation of the notion of “cultural trait”, however, requires the interrogation of many disciplines, from cultural anthropology to linguistics, from psychology to archaeology to musicology. The very possibility of assuming the existence of cultural traits is not granted. In order to start a wide interdisciplinary confrontation, we need a sufficiently loose definition of a cultural trait as any trait whose production in individuals depends, to some extent, on social learning; and we need a deflationary interpretive horizon where cultural traits are not expected to provide an exhaustive theory of culture and cultural change. But from there, we can go a long way if each of the involved disciplines enters the debate with a self-presenting attitude, emphasizing its own methodological practices, and explaining whether and how cultural traits have a role in its own research programs and epistemic goals. Are there differences in aspects of culture that are studied by different disciplines? What definitions of cultural traits are on the table? How do we delimit a trait? How is the problem declined at different observational scales, and which scales are most in focus? Do traits travel in geographical space, and how? Are there other relevant spaces? How are traits modified in their diffusion? Is it possible and useful to build models of this diffusion? Only a strong multidisciplinary perspective can help to clarify these problems about cultural traits, by means of which we understand our precious heritage, cultural diversity. (shrink)

Until the late 19th century scientists almost always assumed that the world could be described as a rule-based and hence deterministic system or as a set of such systems. The assumption is maintained in many 20th century theories although it has also been doubted because of the breakthrough of statistical theories in thermodynamics (Boltzmann and Gibbs) and other fields, unsolved questions in quantum mechanics as well as several theories forwarded within the social sciences. Until recently it has furthermore been (...) assumed that a rule-based and deterministic system was also predictable if only the rules were known, but this assumption has now been undermined by modern chaos-theory describing rule-based and deterministic, but unpredictable systems, while catastrophe-theory delivers a set of types describing various kinds of instability and conditions for the stability of a given system. Hence the main trait in the theoretical development in the 20th-century science can be described as a basic modification and limitation of some of the fundamental and strong assumptions forwarded in the previous epochs of modern science. Ironically, the very same process has been a process in which the human capacity to intervene in nature has expanded dramatically and mainly with the help of the very same theories, and not least because they allow nature to be described and made manipulable on a lower level and a more fine-grained scale. While the overall theoretical consistency between the various theories has gone, the reach of human intervention in nature has increased based on quite new dimensions whether in the area of physics (e.g.: energy technologies, chemical technologies, nanotechnologies etc.) or biology (ge¬netic manipulation) or in the area of psychology, sociology and culture (artificial simulations of mental processes, new means of communication, implying changes in the social infrastructure and cultural behaviour etc.). While some of these changes and new conditions can be reflected from within the conceptual framework of rule-based systems, albeit more complex than formerly recognized, others seem to give rise to the question of whether there are »systems« and relations between different systems in the world which are not rule-based? For instance, it seems to be obvious that the notion of instability represents a major conceptual break with former theories of rule-based systems, as the stability of the latter is an axiomatically given property implied in the very notion of rule-based systems, while instability can only be the result of external influence which should be explained as the result of another rule-based sy¬stem. While there are no difficulties implied concerning the stability of rule-based systems, the notion of unstable states of a system raises the question of how there can be a system at all if there are no invariant stabilising principles? This is the first question which I will address. And I shall do so by taking two examples of such systems as my point of departure. The first example will be the computer and the second will be ordinary language. In both cases I will argue that the stability of these systems (which are both defined by the existence/presence of human intentions) are provided by the help of - differently organised - redundancy functions which both allow the maintenance of systems in unstable macro-states, suspension of previous rules, underdetermination and overdetermination and generation/emergence/creation of new rules more or less independent of previous rules by the help of optional recursions to the permanently accessible underlying levels as for instance the level of binary representation in computers. Since the notion of redundancy is both controversial as such and often avoided, the concept is discussed (as defined in Claude Shannon's mathematical theory of information and in the semiotic framework of J. J. Greimas) and leading to a more general definition in which the redundancy functions serve to overcome noisy conditions, but at the cost of rule-based stability, determination, and predictability. A second question will be how the notion of rule-generating systems relates to the notion of anticipatory systems and it will be argued that rule-generating systems share some features with an¬ticipatory systems and that the former from a certain viewpoint can be seen as a subclass of the latter, although anticipative features are not necessarily a part of the definition of rule-generating systems. On the other hand, it will be discussed whether anticipatory systems which are not rule-generating systems can exist and it will be argued that the capacity to anticipate is strongly limited if it is not part of a rule-generating system. Therefore, it is concluded that the most powerful anticipatory systems need to be rule-generating systems. (shrink)

This study provides a basic introduction to agent-based modeling (ABM) as a powerful blend of classical and constructive mathematics, with a primary focus on its applicability for social science research. The typical goals of ABM social science researchers are discussed along with the culture-dish nature of their computer experiments. The applicability of ABM for science more generally is also considered, with special attention to physics. Finally, two distinct types of ABM applications are summarized in order to illustrate concretely the duality (...) of ABM: Real-world systems can not only be simulated with verisimilitude using ABM; they can also be efficiently and robustly designed and constructed on the basis of ABM principles. (shrink)

All humans share a universal, evolutionarily ancient approximate number system (ANS) that estimates and combines the numbers of objects in sets with ratio-limited precision. Interindividual variability in the acuity of the ANS correlates with mathematical achievement, but the causes of this correlation have never been established. We acquired psychophysical measures of ANS acuity in child and adult members of an indigene group in the Amazon, the Mundurucú, who have a very restricted numerical lexicon and highly variable access to mathematics education. (...) By comparing Mundurucú subjects with and without access to schooling, we found that education significantly enhances the acuity with which sets of concrete objects are estimated. These results indicate that culture and education have an important effect on basic number perception. We hypothesize that symbolic and nonsymbolic numerical thinking mutually enhance one another over the course of mathematics instruction. (shrink)

What endogenous factors contribute to minority (Red Queen) or majority (Red King) domination under conditions of coercive bargaining? We build on previous work demonstrating minority disadvantage in non-coercive bargaining games to show that under neutral initial conditions, majorities are advantaged in high conflict situations, and minorities are advantaged in low conflict games. These effects are a function of the relationship between (1) relative proportions of the majority and minority groups and (2) costs of conflict. Although both Red King and Red (...) Queen effects can occur, we further show that agents’ increased initial propensity toward conflict advantages majorities. (shrink)

The mathematical universe hypothesis is a theory that the physical universe is not merely described by mathematics, but is mathematics, specifically a mathematical structure. Our research provides evidence that the mathematical structure of the universe is biological in nature and all systems, processes, and objects within the universe function in harmony with biological patterns. Living organisms are the result of the universe’s biological pattern and are embedded within their physiology the patterns of this biological universe. Therefore physiological patterns in (...) living organisms can be used as models to structurally map analogies from the biological domain to any target domain to reveal and understand the biological nature of the target domain. Our paper explores various analogies, structurally mapping a red blood cell to a cup; proteins produced from ribosomes to music produced from instruments; a beating heart to the melting and freezing of Antartica; cells, tissue, organs and blood, to people, organizations, industries, and money, and; bio-economic concepts in cellular society to socioeconomic concepts in human society. It also discusses how phenomena in cellular mitosis can help explain phenomena in the universe, such as black holes, dark matter, dark energy, and the structure of the universe. Building upon the concept of perennial wisdom, our research has provided evidence that the ideas of a biological universe were expressed across many past cultures and historical periods. The implications of this theory are vast, encompassing fields such as physics, science, philosophy, religion, law, economics, politics, and engineering, thus serving as a unifying theory for all knowledge. Our theory is supported by meta-analysis of scientific, historic, and religious literature, observations and first principles logic. (shrink)

This paper is part of a project that is based on the notion of a dialectical system, introduced by Magari as a way of capturing trial and error mathematics. In Amidei et al. (2016, Rev. Symb. Logic, 9, 1–26) and Amidei et al. (2016, Rev. Symb. Logic, 9, 299–324), we investigated the expressive and computational power of dialectical systems, and we compared them to a new class of systems, that of quasi-dialectical systems, that enrich Magari’s systems (...) with a natural mechanism of revision. In the present paper we consider a third class of systems, that of p-dialectical systems, that naturally combine features coming from the two other cases. We prove several results about p-dialectical systems and the sets that they represent. Then we focus on the completions of first-order theories. In doing so, we consider systems with connectives, i.e. systems that encode the rules of classical logic. We show that any consistent system with connectives represents the completion of a given theory. We prove that dialectical and q-dialectical systems coincide with respect to the completions that they can represent. Yet, p-dialectical systems are more powerful; we exhibit a p-dialectical system representing a completion of Peano Arithmetic that is neither dialectical nor q-dialectical. (shrink)

Over the past few years we have seen an increasing number of legal proceedings related to inappropriately implemented technology. At the same time career paths have diverged from the foundation of statistics out to Data Scientist, Machine Learning and AI. All of these new branches being fundamentally branches of statistics and mathematics. This has meant that formal training has struggled to keep up with what is required in the plethora of new roles. Mathematics as a taught subject is still based (...) in decades old teaching specifications and has not been updated centrally as a curriculum to include new technologies, coding or ethics. This subject area is firmly split between ICT and Mathematics in secondary school, continuing on to be split between Computer Science and Mathematics at University. As we move forwards with technology we see these once seperate fields becoming increasingly intertwined. We propose that existing provision for concepts such as ethics and societal responsibility in analysis currently exist but have not been incorporated into the mainstream curriculum of School or University. This is partially due to the split between fields in an educational setting but also the speed with which education is able to keep up with Industry and its requirements. Principles and frameworks of socially responsible modelling beginning at school level means that ethics and real-life modelling are introduced much earlier than normal. Integrating these concepts with philosophical principles of society and politics ensures a suitable background for future modellers and users of technology to draw on. Modelling is currently undertaken in technical sciences at University but the Subject Benchmark Statements are not current (Subject Benchmark Statements describe the nature of study and the academic standards expected of graduates in specific subject areas. They show what graduates might reasonably be expected to know, do and understand at the end of their studies). Even in 2019 the UK did not yet have Benchmark Statements that discuss the learning to be done in Higher Education around AI and advanced Machine Learning. Where there is provision for AI and Data Science within degree courses ethics is not generally highlighted as a key concept. As such there can be a lack of focus on the teaching of modelling or ethics as specific skills. The skills required to use a basic statistical model, for example would not be sufficient to start from scratch and build an ethical model reflecting real-world scenarios with which to inform policy or organisational decision making. This is a skill in itself and includes such aspects as awareness of data quality, ethics, user implementation problems, context and an understanding of the environment that the model is being created in. As the field of analytics has progressed so quickly in the last decade modules such as those covering AI have simply been bolted on to Maths or Computing degrees rather than being fully detailed as key areas of study or driving new, more integrated courses of study. This paper posits that gaps at primary, secondary and tertiary educational levels need to be addressed. Implementing and integrating key concepts from school level is essential so that areas such as assumptions, caveats, quality assurance and answering the right questions with constructive challenge become a cultural fixture. This not only helps developers of technology but users of rapidly developing technology also. In addition, leadership and soft skills as part of this education will ensure that a cultural shift can take place and promote continuous improvement in analysis within organisations. The addition of key concepts throughout the educational system and the updating of potentially outdated curriculums is key to ensuring a functional society. A society where every citizen is a user of tech and those that develop it can be ethical and socially responsible in its development. (shrink)

In their recent paper on “Challenges in mathematical cognition”, Alcock and colleagues (Alcock et al. [2016]. Challenges in mathematical cognition: A collaboratively-derived research agenda. Journal of Numerical Cognition, 2, 20-41) defined a research agenda through 26 specific research questions. An important dimension of mathematical cognition almost completely absent from their discussion is the cultural constitution of mathematical cognition. Spanning work from a broad range of disciplines – including anthropology, archaeology, cognitive science, history of science, linguistics, philosophy, and psychology – (...) we argue that for any research agenda on mathematical cognition the cultural dimension is indispensable, and we propose a set of exemplary research questions related to it. (shrink)

Husserl’s philosophy, by the usual account, evolved through three stages: 1. development of an anti-psychologistic, objective foundation of logic and mathematics, rooted in Brentanian descriptive psychology; 2. development of a new discipline of "phenomenology" founded on a metaphysical position dubbed "transcendental idealism"; transformation of phenomenology from a form of methodological solipsism into a phenomenology of intersubjectivity and ultimately (in his Crisis of 1936) into an ontology of the life-world, embracing the social worlds of culture and history. We show that this (...) story of three revolutions can provide at best a preliminary orientation, and that Husserl was constantly expanding and revising his philosophical system, integrating views in phenomenology, ontology, epistemology and logic with views on the nature and tasks of philosophy and science as well as on the nature of culture and the world in ways that reveal more common elements than violent shifts of direction. We argue further that Husserl is a seminal figure in the evolution from traditional philosophy to the characteristic philosophical concerns of the late twentieth century: concerns with representation and intentionality and with problems at the borderlines of the philosophy of mind, ontology, and cognitive science. (shrink)

Computational tools might tempt us to renounce complete cer- tainty. By forgoing of rigorous proof, we could get (very) probable results for a fraction of the cost. But is it really true that proofs (as we know and love them) can lead us to certainty? Maybe not. Proofs do not wear their correct- ness on their sleeve, and we are not infallible in checking them. This suggests that we need help to check our results. When our fellow mathematicians will be (...) too tired or too busy to scrutinize our putative proofs, computer proof assistants could help. But feeding a mathematical argument to a computer is hard. Still, we might be willing to undertake the endeavor in view of the extra perks that formalization may bring—chiefly among them, an enhanced mathematical understanding. (shrink)

A special issue of the International Journal in Information Science and Engineering “Neutrosophic Sets and Systems” (vol. 71/2024) is dedicated to the Conference on NeutroGeometry, NeutroAlgebra, and Their Applications, organized by the Latin American Association of Neutrosophic Sciences. This event, which took place on August 12-14, 2024, in Havana, Cuba, was made possible by the valuable collaboration of the University of Havana, the University of Physical Culture and Sports Sciences "Manuel Fajardo," the José Antonio Echeverría University of Technology, University (...) of Informatics Sciences and the Cuban Academy of Sciences among other institutions. In 2019 Smarandache generalized the classical Algebraic Structures to NeutroAlgebraic Structures (or NeutroAlgebras) {whose operations and axioms are partially true, partially indeterminate, and partially false} as extensions of Partial Algebra, and to AntiAlgebraic Structures (or AntiAlgebras) {whose operations and axioms are totally false} and on 2020 he continued to develop them. The NeutroAlgebras & AntiAlgebras are a new field of research, which is inspired from our real world. In classical algebraic structures, all operations are 100% well-defined, and all axioms are 100% true, but in real life, in many cases these restrictions are too harsh, since in our world we have things that only partially verify some operations or some laws. Similarly, a classical Geometry structure has all axioms totally (100%) true. A NeutroGeometry structure has some axioms that are only partially true, and no axiom is totally (100%) false. Whereas an AntiGeometry structure has at least one axiom that is totally (100%) false. And in general, in any field of knowledge one has: Structure, NeutroStructure, and AntiStructure which were inspired from our real world where the laws (axioms) do not equally apply to all people and in the same degree. This special issue aims to highlight the most recent advances and applications in the fields of NeutroGeometry and NeutroAlgebra, two areas that are at the forefront of contemporary mathematical and scientific thought. During the conference, the mathematical foundations and practical applications of these disciplines were explored, as well as their relevance in the MultiAlism system and other interdisciplinary areas. The content of this special issue has been carefully selected to reflect the diversity and depth of the topics discussed at the conference. This event and the subsequent publication of these works underline the growing importance of neutrosophic theories in the current scientific landscape. We are confident that the ideas and discoveries shared in these pages will be of great value to researchers, academics, and professionals interested in these innovative areas of knowledge. (shrink)

In these days, there is an increasing technological development in intelligent tutoring systems. This field has become interesting to many researchers. In this paper, we present an intelligent tutoring system for teaching mathematics that help students understand the basics of math and that helps a lot of students of all ages to understand the topic because it's important for students of adding and subtracting. Through which the student will be able to study the course and solve related problems. An (...) evaluation of the intelligent tutoring systems was carried out and the results were encouraging. (shrink)

The paper portrays the influence of major philosophical ideas on the 1935 debates on quantum theory that reached their climax in the paper by Einstein, Podosky and Rosen, and describes the relevance of these ideas to the vast impact of the paper. I claim that the focus on realism in many common descriptions of the debate misses important aspects both of Einstein's and Bohr's thinking. I suggest an alternative understanding of Einstein's criticism of quantum mechanics as a manifestation of the (...) same methodological principles that served him in the construction of the special and the general theories of relativity. These principles address, in a very specific way, the relation of the theoretical mathematical representations to the represented physical systems. These ideas, I claim, played a key role in the influence of the paper on later works that changed our understanding of quantum theory despite the rejection of EPR's central conclusion. (shrink)

Contrary to chimpanzees and bonobos, humans display long-term exclusive relationships between males and females. Probably all human cultures have some kind of marriage system, apparently designed to protect these exclusive relationships and the resulting offspring in a potentially sexual competitive environment. Different hypotheses about the origin of human pair-bonds are compared and it is shown how they may refer to different phases of human evolution.

The information regime is mediated by the culture of the electronic device. It is characterized by the control of the deluded citizen through the deployment of freedom, thereby nullifying the core issue of human life: freedom. Through phenomenological-hermeneutic methodology (Heidegger, 2002), this work starts from the world of digital life to direct the interpretation towards digital governance, all of which appears as a hermeneutic horizon the information regime. It is concluded that in this new social order the political and all (...) other orders that arise from interaction are governed by a capitalism of emotions. (shrink)

Geometry, etymologically the “science of measuring the Earth”, is a mathematical formalization of space. Just as formal concepts of number may be rooted in an evolutionary ancient system for perceiving numerical quantity, the fathers of geometry may have been inspired by their perception of space. Is the spatial content of formal Euclidean geometry universally present in the way humans perceive space, or is Euclidean geometry a mental construction, specific to those who have received appropriate instruction? The spatial content of the (...) formal theories of geometry may depart from spatial perception for two reasons: first, because in geometry, only some of the features of spatial figures are theoretically relevant; and second, because some geometric concepts go beyond any possible perceptual experience. Focusing in turn on these two aspects of geometry, we will present several lines of research on US adults and children from the age of three years, and participants from an Amazonian culture, the Mundurucu. Almost all the aspects of geometry tested proved to be shared between these two cultures. Nevertheless, some aspects involve a process of mental construction where explicit instruction seem to play a role in the US, but that can still take place in the absence of instruction in geometry. (shrink)

Bribing doctors for preferential treatment is rampant in the healthcare system of developing countries like Vietnam. Although bribery raises the out-of-pocket expenditures of patients, it is so common to be deemed an “envelope culture.” Given the little understanding of the underlying mechanism of the culture, this study employed the mindsponge theory for reasoning the mental processes of both patients and doctors for why they embrace the “envelope culture” and used the Bayesian Mindsponge Framework (BMF) analytics to validate our reasoning. Analyzing (...) responses from 1042 Vietnamese patients, we discovered that bribing doctors can help patients reduce the destitution risk induced by treatment. Such effect of doctor bribery remains consistent among patients that have to pay high daily costs (e.g., accommodation and subsistence fees) regardless of their employment status. Nevertheless, for patients with no or unstable jobs, their risks of destitution increase if they have to pay more thank-you money. These findings suggest that doctor bribery is an adaptive strategy for patients in an environment where the healthcare supply cannot meet the actual demand. Moreover, healthcare equity is greatly exacerbated due to the envelope culture, as vulnerable individuals are exposed to a greater threat of poverty. At the same time, those with good economic conditions get preferential treatment by paying a higher amount of thank-you money. Healthcare workers’ ethics must be the top priority for an equitable and proper healthcare system. (shrink)

Abstract We examine the construction of electromagnetism in its current form, and in an alternative form, from a point of view that combines a minimal realism with strict rational demands. We begin by discussing the requests of reason when constructing a theory and next, we follow the historical development as presented in the record of original publications, the underlying epistemology (often explained by the authors) and the mathematical constructions. The historical construction develops along socio-political disputes (mainly, the reunification of Germany (...) and the second industrial revolution), epistemic disputes (at least two demarcations of science in conflict) and several theories of electromagnetism. Such disputes resulted in the militant adoption of the ether by some, a position that expanded in parallel with the expansion of Prussia. This way of thinking was facilitated by the earlier adoption of a standpoint that required, as a condition for understanding, the use of physical hypothesis in the form of analogies; an attitude that is antithetic to Newton's “hypotheses non fingo”. While the material ether was finally abandoned, the epistemology survived in the form of “substantialism” and a metaphysical ether: the space. The militants of the ether attributed certainties regarding the ether to Faraday and Maxwell, when they only expressed doubts and curiosity. Thus, the official story is not the real history. This was achieved by the operation of detaching Maxwell's electromagnetism from its construction and introducing a new game of formulae and interpretations. Large and important parts of Maxwell work are today not known, as for example, the rules for the transformation of the electromagnetic potentials between moving systems. When experiments showed that all the theories based in the material ether were incorrect, a new interpretation was offered: Special Relativity (SR). At the end of the transformation period a pragmatic view of science, well adapted to the industrial society, had emerged, as well as a new protagonist: the theoretical physicist. The rival theory of delayed action at distance initiated under the influence of Gauss was forgotten in the midst of the intellectual warfare. The theory is indistinguishable in formulae from Maxwell's and its earlier versions are the departing point of Maxwell for the construction of his equations. We show in a mathematical appendix that such (relational) theory can incorporate Lorentz' contributions as well as Maxwell's transformations and C. Neumann's action, without resource to the ether. Demarcation criteria was further changed at the end of the period making room for habits and intuitions. When these intuited criteria are examined by critical reason (seeking for the fundaments) they can be sharpened with the use of the Non Arbitrariness Principle, which throws light over the arbitrariness in the construction of SR. Under a fully rational view SR is not acceptable, it requires to adopt a less demanding epistemology that detaches the concept from the conception, such as Einstein's own view in this respect, inherited from Hertz. In conclusion: we have shown in this relevant exercise how the reality we accept depends on earlier, irrational, decisions that are not offered for examination but rather are inherited from the culture. (shrink)

This article analyzes the historical development of the philosophical logic syntax from the standpoint of the unity of historical and logical methods. According to this perspective, there are three types of logical syntax: the elementary subject-predicate, the modified definitivespecificative, and the standard propositional-functional. These types are generalized in the grammatical and mathematical styles of logical syntax. The main attention is paid to two scientific revolutions in elementary subject-predicate syntax, which led to the emergence of modified definitive-specific and standard propositional-functional syntaxes (...) and created the syntactic conditions for the development of contemporary philosophical logic. The specifics of contemporary philosophical logic and the methodological possibilities of its application to philosophical discourse are studied. The article aims to reevaluate the undeservedly forgotten systems of philosophical logic of the continental tradition, created by such prominent representatives as Aristotle, G.W.F. Hegel, and E. Husserl, and to actualize these logics in the context of contemporary philosophical culture. The potential of the above-mentioned logics is not fully involved in the philosophical discourse of modernity, primarily because they primarily used an imperfect elementary subject-predicate syntax and modified definitive-specificative syntax as its slightly improved version. Both syntaxes have one thing in common: the grammatical style of sentence structure. Nevertheless, they also have one common flaw – a high dependence on grammar formalism. As a result, the interaction between these syntaxes and Frege’s standard propositional-functional syntax is impossible, because the latter is based on mathematical formalism, which operates on the philosophical logic of the analytic tradition. The article substantiates the way to solve this problem by constructing a modified subject-predicate syntax of contemporary philosophical logic. This syntax provides information interaction between Aristotle’s elementary subject-predicate syntax, and Frege’s standard propositional-functional syntax based on Hegel’s modified definitive-specificative syntax. The proposed solution to this problem can create new opportunities for complementarity and mutual enrichment between the philosophical logic of continental and analytical traditions. The theoretical basis for the construction and study of contemporary philosophical logic is a functional analysis of contemporary symbolic logic, which improves the grammatical analysis of traditional formal logic. Functional-grammatical analysis is a way to rehabilitate the philosophical logic of the continental tradition. The novelty of this paper lies in the substantiation of the modified subjectpredicate syntax of contemporary philosophical logic. It makes it possible to establish a dialogue between continental and analytical traditions, which is designed to promote the further development of philosophy. (shrink)

The component structures of two distinct neuropsychological systems are described. "System-Y" depends upon "system-X" which, on the other hand, can operate independently of system-Y. System-X provides a matrix upon which system-Y must operate, and, system-Y is transformed by the operations of system-X. In addition these neuropsychological structures reverberate in political history and in the cosmos. The most fundamental structure in the soul, in society, and in the cosmos, has the form of a conical spiral. It can be described mathematically (...) as an harmonic system and mythologically in terms of the birth, marriage and death of the divine-king. ;System-Y corresponds to the neocortex. System-X corresponds to the region below the cortex including the limbic brain. Many of the essential structures of system-Y are captured by Plato's image of the helmsman: orientation, locomotion, manual control and dexterity, visual guidance, verbal command, intention, and volition. System-X on the other hand has been systematically neglected by Western culture, beginning with Plato. ;The dissertation builds upon Yakovlev's distinction between "teleokinesis," "ectokinesis" and "endokinesis." "Teleokinesis" refers to goal-directed action in external space, and belongs to system-Y. Ectokinesis and endokinesis are components of system-X. "Endokinesis" refers to movements within the body. "Ectokinesis" refers to the emotions, which are expressions of endokinesis. The mechanics of ectokinesis is that of an harmonic or vibrational system, as is the mechanics of a musical instrument. ;Within a trance the structure of system-Y is temporarily altered, such that system-X enters the foreground of awareness. Because ectokinesis is analogous to music cultures inspired by trance experience understand the universe in terms of music. The structure of ectokinesis in a trance is that of a conical spiral. Plato inherited the mystical traditions of the ancient Near East but replaced the spiral of emotions with a spiral of ideas , by understanding the axis of the cone as the paradigmatic dimension, and the angular rotation of the spiral as the syntagmatic dimension, of language. Finally I explain how the mythology and political structure of theocratic society imitated the neuropsychological structures of trance experience. (shrink)

The current appeal of non-standard economic alternatives is backgrounded against the vulnerability of mainstream capitalism to meltdown and crisis as shown in recent times. There is an increasing number of governments, institutions, and civil societies (NGOs) that have been advocating economic systems, structures, or dynamics that would promote the good of the human person (dignity, personhood, values, and worth). People have started to realize that doing economics is not always within the realm of rationalized judgments and mathematized calculations (highly (...) impersonal) but must look after the human person, at all costs. This paper attempts to contribute to this agendum by employing an interdisciplinary dialogue between theology and economics; drawing a moral-cultural framework towards a compassion-based economics. Together with the positive traits of today’s economic alternatives and the salient features of Jesus’ praxis of compassion, this paper would offer fourteen (14) criteria as basis for what could be the most feasible base/locus for an economics of compassion. Eventually, what has been considered as the suitable base/locus is the Basic Ecclesial Communities (BECs). Hence, a BEC-based Economics of Compassion or BEC-EC. (shrink)

In this paper, a formal theory is presented that describes syntactic and semantic mechanisms of philosophical discourses. They are treated as peculiar language systems possessing deep derivational structures called architectonic forms of philosophical systems, encoded in philosophical mind. Architectonic forms are constituents of more complex structures called architectonic spaces of philosophy. They are understood as formal and algorithmic representations of various philosophical traditions. The formal derivational machinery of a given space determines its class of all possible architectonic forms. (...) Some of them stand under factual historical philosophical systems and they organize processes of doing philosophy within these systems. Many architectonic forms have never been realized in the history of philosophy. The presented theory may be interpreted as falling under Hegel’s paradigm of comprehending cultural texts. This paradigm is enriched and inspired with Propp’s formal, morphological view on texts. The peculiarity of this modification of the Hegel-Propp paradigm consists of the use of algebraic and algorithmic tools of modeling processes of cultural development. To speak metaphorically, the theory is an attempt at the mathematical and logical history of philosophy inspired by the Internet metaphor. And that is why it belongs to the tradition of doing metaphilosophy in The Lvov-Warsaw School, which is continued today mainly by Woleński, Pelc, Perzanowski, and Jadacki. (shrink)

(PTOJ) - The cultural value system is one of the core and fundamental value systems in Vietnam and is part of the foundation to ensure the country's sustainable development. This article analyzes the building of a Vietnamese cultural value system in the context of the Fourth Industrial Revolution, which has a significant impact all aspects of social life, including the cultural sector.

Western science claims to provide unique, objective information about the world. This is supported by the observation that peoples across cultures will agree upon a common description of the physical world. Further, the use of scientific instruments and mathematics is claimed to enable the objectification of science. In this work, carried out by reviewing the scientific literature, the above claims are disputed systematically by evaluating the definition of physical reality and the scientific method, showing that empiricism relies ultimately upon the (...) human senses for the evaluation of scientific theories and that measuring instruments cannot replace the human sensory system. Nativist and constructivist theories of human sensory development are reviewed, and it is shown that nativist claims of core conceptual knowledge cannot be supported by the findings in the literature, which shows that perception does not simply arise from a process of maturation. Instead, sensory function requires a long process of learning through interactions with the environment. To more rigorously define physical reality and systematically evaluate the stability of perception, and thus the basis of empiricism, the development of the method of dimension analysis is reviewed. It is shown that this methodology, relied upon for the mathematical analysis of physical quantities, is itself based upon empiricism, and that all of physical reality can be described in terms of the three fundamental dimensions of mass, length and time. Hereafter the sensory modalities that inform us about these three dimensions are systematically evaluated. The following careful analysis of neuronal plasticity in these modalities shows that all the relevant senses acquire from the environment the capacity to apprehend physical reality. It is concluded that physical reality is acquired rather than given innately, and leads to the position that science cannot provide unique results. Rather, those it can provide are sufficient for a particular environmental setting. (shrink)

It has become a fact that fluency and competency in utilizing the advancement of technology, specifically the computer and the internet is one way that could help in facilitating learning in mathematics. This study investigated the effects of Dynamic Geometry Software (DGS) and Computer Algebra Systems (CAS) in teaching Mathematics. This was conducted in Zamboanga del Sur National High School (ZSNHS) during the third grading period of the school year 2015-2016. The study compared the achievement and attitude towards Mathematics (...) between those students taught with DGS and CAS and those students who were taught without DGS and CAS. A quasi-experimental pretest-posttest control group design was used with two groups which was matched according to their mathematical level. An achievement test was developed and administered to assess the students’ achievement in Mathematics. Aiken’s attitude scale was also used to assess the students’ attitude towards Mathematics. The data were treated with One-Way Analysis of Covariance (ANCOVA) and t-test at 0.05 level of significance. The study revealed a significant difference between the mathematics achievement between students taught with DGS and CAS and those who were taught without it. The integration of DGS and CAS in Mathematics lessons leads to better academic achievement result compared with that of the conventional method of teaching. Moreover, there was no significant difference on the attitude level of the students between the two groups. (shrink)

My central research focus over the past 30 years has been the articulation of what I call a radically temporal approach to philosophy. In the papers below, written between 2001 and 2022, I treat the varying ways in which radically temporal thinking manifests itself in the phenomenological perspectives of Edmund Husserl, Martin Heidegger and Eugene Gendlin. I also discuss Jacques Derrida's deconstructive project and George Kelly's personal construct theory as examples of radically temporal thinking. With the aim of clarifying and (...) further defining the nature of this family of orientations, I have delineated the important ways in which it differs from a range of interlinked approaches in philosophy and psychology that includes hermeneutic and radical constructivisms, social constructionism, 4EA (Embodied, Embedded, Enactive, Extended, and Affective) cognition, Merleau-Ponty's phenomenology of corporeal intersubjectivity, autopoietic self-organizing systems theory and American pragmatism. Among the authors whose work I have submitted to critique from the radically temporal perspective are: Francisco Varela (autopoietic self-organizing systems), Shaun Gallagher, Evan Thompson, Matthew Ratcliffe, Maxine Sheets-Johnstone, Dan Zahavi, Hanne De Jaegher, Michel Bitbol, Thomas Fuchs (enactive, embodied ('4EA') cognition), Gilles Deleuze (Deleuzian biopolitics), Ken Gergen and John Shotter ( social constructionism), Kym Maclaren ( critical phenomenology) and Jan Slaby (critical neuroscience). I argue that these authors' accounts of the relation between affect, motivation and intention, attention , reflective and pre-reflective self-consciousness, the basis of mathematical naturalism and sensori-motor models of behavior, and the relation between the body, language and culture remain burdened by traditional presuppositions that the radically temporal philosophies of Heidegger et al put into question. (shrink)

Dans 'Godel’s Way', trois éminents scientifiques discutent de questions telles que l’indécidabilité, l’incomplétude, le hasard, la calculabilité et la paraconsistence. J’aborde ces questions du point de vue de Wittgensteinian selon lesquelles il y a deux questions fondamentales qui ont des solutions complètement différentes. Il y a les questions scientifiques ou empiriques, qui sont des faits sur le monde qui doivent être étudiés de manière observationnelle et philosophique quant à la façon dont le langage peut être utilisé intelligiblement (qui incluent certaines (...) questions en mathématiques et en logique), qui doivent être décidés en regardant un comment nous utilisons réellement des mots dans des contextes particuliers. Lorsque nous obtenons clair sur le jeu de langue que nous jouons, ces sujets sont considérés comme des questions scientifiques et mathématiques ordinaires comme les autres. Les idées de Wittgenstein ont rarement été égalées et jamais dépassées et sont aussi pertinentes aujourd’hui qu’elles l’étaient il y a 80 ans lorsqu’il a dicté les Livres Bleus et Brown. Malgré ses défauts, vraiment une série de notes plutôt qu’un livre fini, c’est une source unique du travail de ces trois savants célèbres qui travaillent aux confins de la physique, des mathématiques et de la philosophie depuis plus d’un demi-siècle. Da Costa et Doria sont cités par Wolpert (voir ci-dessous ou mes articles sur Wolpert et mon examen de Yanofsky 'The Outer Limits of Reason') depuis qu’ils ont écrit sur le calcul universel, et parmi ses nombreuses réalisations, Da Costa est un pionnier dans la paraconsistence. -/- Ceux qui souhaitent un cadre complet à jour pour le comportement humain de la vue moderne de deux système peuvent consulter mon livre 'The Logical Structure of Philosophy, Psychology, Mind and Language in Ludwig Wittgenstein and John Searle' 2nd ed (2019). Ceux qui s’intéressent à plus de mes écrits peuvent voir «Talking Monkeys --Philosophie, Psychologie, Science, Religion et Politique sur une planète condamnée --Articles et revues 2006-2019 » 3e ed (2019) et Suicidal Utopian Delusions in the 21st Century 4th ed (2019) et autres. (shrink)

Scientists use models to know the world. It i susually assumed that mathematicians doing pure mathematics do not. Mathematicians doing pure mathematics prove theorems about mathematical entities like sets, numbers, geometric figures, spaces, etc., they compute various functions and solve equations. In this paper, I want to exhibit models build by mathematicians to study the fundamental components of spaces and, more generally, of mathematical forms. I focus on one area of mathematics where models occupy a central role, namely homotopy theory. (...) I argue that mathematicians introduce genuine models and I offer a rough classification of these models. (shrink)

We review some results in the theory of non-relativistic quantum unstable systems. We account for the most important definitions of quantum resonances that we identify with unstable quantum systems. Then, we recall the properties and construction of Gamow states as vectors in some extensions of Hilbert spaces, called Rigged Hilbert Spaces. Gamow states account for the purely exponential decaying part of a resonance; the experimental exponential decay for long periods of time physically characterizes a resonance. We briefly discuss (...) one of the most usual models for resonances: the Friedrichs model. Using an algebraic formalism for states and observables, we show that Gamow states cannot be pure states or mixtures from a standard view point. We discuss some additional properties of Gamow states, such as the possibility of obtaining mean values of certain observables on Gamow states. A modification of the time evolution law for the linear space spanned by Gamow shows that some non-commuting observables on this space become commuting for large values of time. We apply Gamow states for a possible explanation of the Loschmidt echo. (shrink)

So-called ‘distinctively mathematical explanations’ (DMEs) are said to explain physical phenomena, not in terms of contingent causal laws, but rather in terms of mathematical necessities that constrain the physical system in question. Lange argues that the existence of four or more equilibrium positions of any double pendulum has a DME. Here we refute both Lange’s claim itself and a strengthened and extended version of the claim that would pertain to any n-tuple pendulum system on the ground that such explanations are (...) actually causal explanations in disguise and their associated modal conditionals are not general enough to explain the said features of such dynamical systems. We argue and show that if circumscribing the antecedent for a necessarily true conditional in such explanations involves making a causal analysis of the problem, then the resulting explanation is not distinctively mathematical or non-causal. Our argument generalises to other dynamical systems that may have purported DMEs analogous to the one proposed by Lange, and even to some other counterfactual accounts of non-causal explanation given by Reutlinger and Rice. (shrink)

The Philippines is a multicultural society with diverse cultures and beliefs for each indigenous community. This study was designed to determine the level of culturally responsive teaching self-efficacy (CRTSE) of mathematics teachers and to propose a training design. The study utilized an explanatory sequential research design using a survey and focus-grouped discussion and was participated by 65 in-service mathematics teachers. Based on the result, the mathematics teachers' overall level of teaching efficacy in using culturally responsive pedagogy (CRP) is very high. (...) It was also found that teachers’ implementation of CRP that influences teaching self-efficacy includes the use of native language and the use of contextualized and localized examples. It is recommended that mathematics teachers may adopt the use of culturally responsive pedagogies in their respective classes and consider the use of native language and use of contextualized and localized examples to provide a meaningful teaching-learning experience. -/- . (shrink)

This work is a complete mathematical guide to lottery games, covering all of the problems related to probability, combinatorics, and all parameters describing the lottery matrices, as well as the various playing systems. The mathematics sections describe the mathematical model of the lottery, which is in fact the essence of the lotto game. The applications of this model provide players with all the mathematical data regarding the parameters attached to the gaming events and personal playing systems. By applying (...) these data, one can find all the winning probabilities for the play with one line, and how these probabilities change with playing the various types of systems containing several lines, depending on their structure. Also, each playing system has a formula attached that provides the number of possible multiple prizes in various circumstances. Other mathematical parameters of the playing systems and the correlations between them are also presented. The generality of the mathematical model and of the obtained formulas allows their application for any existent lottery and any playing system. Each formula is followed by numerical results covering the most frequent lottery matrices worldwide and by multiple examples predominantly belonging to the 6/49 lottery. The listing of the numerical results in dozens of well-organized tables, along with instructions and examples of using them, makes possible the direct usage of this guide by players without a mathematical background. The author also discusses from a mathematical point of view the strategies of choosing involved in the lotto game. The book does not offer so-called winning strategies, but helps players to better organize their own playing systems and to confront their own convictions with the incontestable reality offered by the direct applications of the mathematical model of the lotto game. As a must-have handbook for any lottery player, this book offers essential information about the game itself and can provide the basis for gaming decisions of any kind. (shrink)

Many biological processes and objects can be described by fractals. The paper uses a new type of objects – blinking fractals – that are not covered by traditional theories considering dynamics of self-similarity processes. It is shown that both traditional and blinking fractals can be successfully studied by a recent approach allowing one to work numerically with infinite and infinitesimal numbers. It is shown that blinking fractals can be applied for modeling complex processes of growth of biological systems including (...) their season changes. The new approach allows one to give various quantitative characteristics of the obtained blinking fractals models of biological systems. (shrink)

What are numbers, and where do they come from? A novel answer to these timeless questions is proposed by cognitive archaeologist Karenleigh A. Overmann, based on her groundbreaking study of material devices used for counting in the Ancient Near East—fingers, tallies, tokens, and numerical notations—as interpreted through the latest neuropsychological insights into human numeracy and literacy. The result, a unique synthesis of interdisciplinary data, outlines how number concepts would have been realized in a pristine original condition to develop into one (...) of the ancient world’s greatest mathematical traditions, a foundation for mathematical thinking today. In this view, numbers are abstract from their inception and materially bound at their most elaborated. The research updates historical work on Neolithic tokens and interpretations of Mesopotamian numbers, challenging several longstanding assumptions about numbers in the process. The insights generated are also applied to the role of materiality in human cognition more generally, including how concepts become distributed across and independent of the material forms used for their representation and manipulation; how societies comprised of average individuals use material structures to create elaborated systems of numeracy and literacy; and the differences between thinking through and thinking about materiality. (shrink)

In this paper, I study how mathematicians are presented in western popular culture. I identify five stereotypes that I test on the best-known modern movies and television shows containing a significant amount of mathematics or important mathematician characters: (1) Mathematics is highly valued as an intellectual pursuit. (2) Little attention is given to the mathematical content. (3) Mathematical practice is portrayed in an unrealistic way. (4) Mathematicians are asocial and unable to enjoy normal life. (5) Higher mathematics is ...

This work is a conceptual analysis of certain recent developments in the mathematical foundations of Classical and Quantum Mechanics which have allowed to formulate both theories in a common language. From the algebraic point of view, the set of observables of a physical system, be it classical or quantum, is described by a Jordan-Lie algebra. From the geometric point of view, the space of states of any system is described by a uniform Poisson space with transition probability. Both these structures (...) are here perceived as formal translations of the fundamental twofold role of properties in Mechanics: they are at the same time quantities and transformations. The question becomes then to understand the precise articulation between these two roles. The analysis will show that Quantum Mechanics can be thought as distinguishing itself from Classical Mechanics by a compatibility condition between properties-as-quantities and properties-as-transformations. -/- Moreover, this dissertation shows the existence of a tension between a certain "abstract way" of conceiving mathematical structures, used in the practice of mathematical physics, and the necessary capacity to specify particular states or observables. It then becomes important to understand how, within the formalism, one can construct a labelling scheme. The “Chase for Individuation” is the analysis of different mathematical techniques which attempt to overcome this tension. In particular, we discuss how group theory furnishes a partial solution. (shrink)

Background: The castor bean is a large grassy or semi-wooden shrub or small tree. Any part of the castor plant parts can suffering from a disease that weakens the ability to grow and eliminates its production. Therefore, in this paper will identify the pests and diseases present in castor culture and detect the symptoms in each disease. Also images is showing the symptom form in this disease. Objectives: The main objective of this expert system is to obtain appropriate diagnosis of (...) the disease. Methods: In this paper, the expert system is designed for the ability of agricultural engineers to detect and diagnose disease of castor like as: seeding blight, alternaria blight, cercospora leaf spot, powdery mildew and wilt. This system presents the disease symptoms, survival and spread, favorable conditions and image for each disease. Clips and Delphi expert system languages are used for designing and implementing the proposed expert system. Results: The expert system in the diagnosis of castor diseases was assessed by farmers and agricultural engineers and they were satisfied and accepted with its quality of performance. Conclusions: The expert system is easy for farmers and people have experience in the plant of castor to detect and diagnosis the symptoms that may face this plant from several disease. (shrink)

Diffusionism in anthropology posits centres of creativity from which things diffuse, such as ideas and innovations. But what sort of place is likely to be such a centre of creativity? I distinguish two cases, the second of which poses a problem for diffusionism.

The city of Kruja dates back to its existence in the 5th and 6th centuries. In the inner city are preserved great historical, cultural, and architectural values that are inherited from generation to generation. In the city interact and coexist three different typologies of dwellings: historic buildings that belong to the XIII, XIV, XV, XIII, XIX centuries (built using the foundations of previous buildings); socialist buildings dating back to the Second World War until 1990; and modern buildings which were (...) built from 1990 onwards. According to the questionnaires, the creation of mathematical models applied to each category will result in contradictory attitudes but also fairy ones based on different percentages. There are underlined 5 quality of life indicators(questions) from a total of 30 questions of the questionnaire, which are involved in mathematical regression and are statistically significant with a significance level p<5% (with a reliability of 95%), which interact for all three categories of buildings. The quality of life indicators: dwelling area, heating mode during winter, level of dwelling improvement, time spent in the dwelling, and monthly electricity payments, are the main actors who will be compared in order to draw conclusions. According to the statistical calculations trend, it is noted that the socialist buildings category does not directly participate in the debate between historic and modern buildings by means of the quality of life indicators (questions). (shrink)

In these days, there is an increasing technological development in intelligent tutoring systems. This field has become interesting to many researchers. In this paper, we present an intelligent tutoring system for teaching mathematics that help students understand the basics of math and that helps a lot of students of all ages to understand the topic because it's important for students of adding and subtracting. Through which the student will be able to study the course and solve related problems. An (...) evaluation of the intelligent tutoring systems was carried out and the results were encouraging. (shrink)

Mathematical diagrams are frequently used in contemporary mathematics. They are, however, widely seen as not contributing to the justificatory force of proofs: they are considered to be either mere illustrations or shorthand for non-diagrammatic expressions. Moreover, when they are used inferentially, they are seen as threatening the reliability of proofs. In this paper, I examine certain examples of diagrams that resist this type of dismissive characterization. By presenting two diagrammatic proofs, one from topology and one from algebra, I show that (...) diagrams form genuine notational systems, and I argue that this explains why they can play a role in the inferential structure of proofs without undermining their reliability. I then consider whether diagrams can be essential to the proofs in which they appear. (shrink)

Contemporary Information Systems management incorporates the need to make explicit the links between semiotics, meaning-making and the digital age. This focus addresses, at its core, pure rationality, that is, the capacity of human interpretation and of human inscription upon reality. Creating the new real, that is the motto. Humans are intrinsically semiotic creatures. Consequently, semiotics is not a choice or an option but something that works like a second skin, establishing limits and permeable linkages between: human thought and human's (...) infinite world of imagination; and human action, with its correspondent infinite world of intentionality, of desire and of unexplored possibilities. Two instances are contrasted as two reading lenses of current business reality: IS governance and industry 4.0. These phenomena correspond to the need to take accountability, transparency and responsibility into account, when designing IS and when using such systems through the ecology of connectivity, Big Data and the Internet of Things. Political, social and cultural dimensions are brought into the equation, when addressing the question of the relevance and adequateness of IS theory and practice to respond to contemporary challenges. The message is that what has already been achieved is but a shadow, a pale vision, of what might be achieved in the age of the new Renaissance. (shrink)

I argue that European schools of thought on memory and memorization were critical in enabling growth of the scientific method. After giving a historical overview of the development of the memory arts from ancient Greece through 17th century Europe, I describe how the Baconian viewpoint on the scientific method was fundamentally part of a culture and a broader dialogue that conceived of memorization as a foundational methodology for structuring knowledge and for developing symbolic means for representing scientific concepts. The principal (...) figures of this intense and rapidly evolving intellectual milieu included some of the leading thinkers traditionally associated with the scientific revolution; among others, Francis Bacon, Renes Descartes, and Gottfried Leibniz. I close by examining the acceleration of mathematical thought in light of the art of memory and its role in 17th century philosophy, and in particular, Leibniz’s project to develop a universal calculus. (shrink)