Review of Raymond L. Wilder, Mathematics as a Cultural System.

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)

Logic has pride of place in mathematics and its 20th century offshoot, computer science. Modern symbolic logic was developed, in part, as a way to provide a formal framework for mathematics: Frege, Peano, Whitehead and Russell, as well as Hilbert developed systems of logic to formalize mathematics. These systems were meant to serve either as themselves foundational, or at least as formal analogs of mathematical reasoning amenable to mathematical study, e.g., in Hilbert’s consistency program. Similar efforts continue, but have been (...) expanded by the development of sophisticated methods to study the properties of such systems using proof and model theory. In parallel with this evolution of logical formalisms as tools for articulating mathematical theories (broadly speaking), much progress has been made in the quest for a mechanization of logical inference and the investigation of its theoretical limits, culminating recently in the development of new foundational frameworks for mathematics with sophisticated computer-assisted proof systems. In addition, logical formalisms developed by logicians in mathematical and philosophical contexts have proved immensely useful in describing theories and systems of interest to computer scientists, and to some degree, vice versa. Three examples of the influence of logic in computer science are automated reasoning, computer verification, and type systems for programming languages. (shrink)

The great chain of being is an ontological conception in which all beings, from inanimate things to God, are ranked on a scale according to their perfectness. This hierarchical scheme, though widely known in the history of ideas, was systematically addressed by Arthur Lovejoy in 1936. The great chain of being as formulated by Lovejoy is composed of three main principles, whose roots can be found in Plato and Aristotle’s philosophies. These principles are “the principle of plenitude”, “the principle of (...) gradation” and “the principle of continuity.” The first principle, the principle of plenitude, was pointed out in Plato’s philosophy and the latter two, the principle of gradation and the principle of continuity, were addressed in Aristotle’s philosophy. According to Lovejoy, these three principles were systematically addressed in Plotinus’s philosophy and became an essential part of Neo-Platonic cosmology. Platon explains the abundance of beings with reference to the absolute goodness of the God in his famous book Timaios. Accordingly, God has absolute goodness and this attribution has given rise to an abundance of beings as goodness requires the existence of things. The other two principles, the principle of gradation and the principle of continuity, were forwarded by Aristotle and through his works affected Western thought. While the principle of gradation refers to the ranking of beings in a chain based on the criteria of their perfection, the principle of continuity is the natural consequence of that ranking in that all beings share at least a minimum level of similarity. Plotinus synthesized and systematized those three principles as an expression of ranked beings specific to emanation theory and added three hypostasis -One, Nous, and Soul- in addition to the natural world addressed in Aristotle’s works. Therefore, we see that beings were ranked from inanimate things to God in Plotinus’s works. This concept of hierarchical order of beings, the great chain of being, affected many cultures and philosophical ideas from Classical Islamic philosophy to the Western tradition. In this article, we confine our subject to only Western thought, including Medieval Christian theology and philosophy, the Renaissance period, and the Age of Enlightenment as well as a peculiar implication and interpretation of the great chain of being specific to modern times. In every period we will deal with just one thinker and their ideas to demonstrate the effect of the great chain of being on those thinkers’ philosophies and systems. In this context, we examined how Thomas Aquinas used the great chain of being to justify some theological and philosophical matters and tried to show how he utilized the principle of continuity effectively to explain the relationship between matter and soul. Marcilio Ficino, a Neo-Platonist philosopher of the Renaissance period, also used the great chain of being to explain the hierarchical order of beings and their ontological relationship to the perfect being, which is God, placing them in a rising line according to their closeness to God. On the other hand, when we come to the Age of Enlightenment we see that the great chain of being continues to be apparent in some philosophical works. One example is John Locke’s famous book An Essay Concerning Human Understanding. Here Locke tries to make sense of the existence of many species of spirits with reference to the great chain of being, especially by using the principle of continuity. This attempt of justification shows us that the great chain of being, as an old philosophical and ontological concept, was still used even in the Enlightenment. Finally, it would be beneficial to address how the chain of being in question was presented and understood in modern times. Unlike the justification of some philosophical or theological subjects, in modern times the hierarchical structure of the great chain of being has been anachronistically read into the theory of evolution with reference to some medieval Muslim philosophers’ works. This approach, however, springs from the figural similarities between the great chain of being and the theory of evolution, although the contents of both theories are completely different. It would be accepted easily that similarities in figure do not necessitate similarities in content. In short, the great chain of being has been very effectively used in the history of philosophy to justify different subjects in different areas such as philosophy and theology. In this article, we address the usages of the chain in question and trace its effects specific to the Western tradition from the ancient period to modern times. (shrink)

In this article culture is understood as the ensemble of systems of classification, assessment, and interaction that establishes a basic community of values in a given social field. We will argue that this is made possible through the institution of fundamental prohibitions understood as mythical points of closure that set the last frontiers of that community by designating what crime is. Exploring these theses, we will see that criminal transgression may be thought of as the actualization of a rigorous otherness. (...) This otherness, however, is nothing but the culture itself in its extreme vectors, its contradictions, and residues. From there we will differentiate three types of crimes: paroxysmal, archaic, and impossible. And we will conclude that the criminal question it is not a ‘social problem’ among others. Rather, it is a fundamental crossroad where the very constitution of any culture is at stake. It is the question of the beginning and end of the societal order and its subjects. (shrink)

In this article culture is understood as the ensemble of systems of classification, assessment, and interaction that establishes a basic community of values in a given social field. We will argue that this is made possible through the institution of fundamental prohibitions understood as mythical points of closure that set the last frontiers of that community by designating what crime is. Exploring these theses, we will see that criminal transgression may be thought of as the actualization of a rigorous otherness. (...) This otherness, however, is nothing but the culture itself in its extreme vectors, its contradictions, and residues. From there we will differentiate three types of crimes: paroxysmal, archaic, and impossible. And we will conclude that the criminal question it is not a ‘social problem’ among others. Rather, it is a fundamental crossroad where the very constitution of any culture is at stake. It is the question of the beginning and end of the societal order and its subjects. (shrink)

This paper aims to identify the decision support systems and their role on the strategic management development in the Universities- Case Study: Islamic University of Gaza. The descriptive approach was used where a questionnaire was developed and distributed to a stratified random sample. (230) questionnaires were distributed and (204) were returned with response rate (88.7%). The most important findings of the study: The presence of a statistically significant positive correlation between the decision support systems and strategic management in the Islamic (...) University in Gaza, and this shows that there is a role for decision support systems in strategic management development. The senior management is convinced of the importance of strategic management of the organization, and this conviction paid to clearly understand the process of the development of strategic management and thus led to a commitment to this process to improve its performance. There is an impact on the strategic management of the capabilities available for the use of decision support systems, and the type of decision support systems used, while there is little effect of top management support for the use of decision support systems. Also, the results showed that there were no statistically significant differences between the averages of the respondents answers attributed to personal data. The research also concluded a series of recommendations: The Islamic University of Gaza need to develop its infrastructure of decision support systems when it develops the strategic management. It should increase its interest in organizational potential through the necessity of a separate unit for decision support systems. As well as increased interest in the physical and technical capabilities available to decision support systems through continuity in keeping pace with technological means and techniques, continued support of senior management in the organization of strategic management for its positive role on decision support systems, that senior management will continue in the organization in creating a culture of strategic management, and it should encourage employees to participate in the strategic management 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)

The purpose of this paper is to show that the mathematics of quantum mechanics is the mathematics of set partitions linearized to vector spaces, particularly in Hilbert spaces. That is, the math of QM is the Hilbert space version of the math to describe objective indefiniteness that at the set level is the math of partitions. The key analytical concepts are definiteness versus indefiniteness, distinctions versus indistinctions, and distinguishability versus indistinguishability. The key machinery to go from indefinite to more definite (...) states is the partition join operation at the set level that prefigures at the quantum level projective measurement as well as the formation of maximally-definite state descriptions by Dirac’s Complete Sets of Commuting Operators. This development is measured quantitatively by logical entropy at the set level and by quantum logical entropy at the quantum level. This follow-the-math approach supports the Literal Interpretation of QM—as advocated by Abner Shimony among others which sees a reality of objective indefiniteness that is quite different from the common sense and classical view of reality as being “definite all the way down”. (shrink)

Husserl and Cassirer stand, according to their own self-understanding, as key 20th century figures in the cultivation of Enlightenment’s principles and views on humanity, culture, and history. In a word, they both understand European culture and history as a story of progress (§ 1). As I see it, central in a culture and its dynamics is its system of values, and a grounded understanding of the issue of progress presupposes an adequate theory of the standing or constitution as well as (...) of the givenness and transvaluation of values. Neither Husserl nor Cassirer, however, actually advanced any such theory. We are still in need of one in order to account for culture’s formation and dynamics in history. Next, I briefly review Husserl’s and Cassirer’s available problematic views on values (§ 2). Then, in § 3, I examine some of the central problems in the traditional approaches to culture and to values. In § 4, I appeal to Köhler’s very interesting Gestalt theoretical approach to values and pinpoint some of its problems. Next, in § 5, I suggest how we could start the research from below, from the level of the organism, which could eventually shed some new light on the problem of value constitution and givenness. Finally, in § 6, I attempt to sketch an explanation for how we can use this new approach to values in order to understand actual cultural formation and its historicity, in a way that goes further than the whiggish philosophy of history. (shrink)

The purpose of cultural competence education for medical professionals is to ensure respectful care and reduce health disparities. Yet as Berger and Miller (2021) show, the cultural competence framework is dated, confused, and self-defeating. They argue that the framework ignores the primary driver of health disparities—systemic racism—and is apt to exacerbate rather than mitigate bias and ethnocentrism. They propose replacing cultural competence with a framework that attends to two social aspects of structural inequality: health and social policy, (...) and institutional-system activity; and two psychological aspects of structural inequality: the clinical encounter, and the epistemic. -/- We agree with the structural approach. To that end, we think it would be fruitful to include attention to physical contributors to structural inequality, namely the material artifacts used in medicine. Devices, tools, and technologies can materialize biases, perpetuate oppression, and contribute to health disparities. Granted, not everything that interests philosophers can be squeezed into medical education. Nevertheless, there are compelling reasons for including the study of material artifacts in education designed to reduce health disparities. First, devices and tools often carry forward biases from the past, and keep biases hidden from plain sight. Second, by studying these artifacts, future clinicians can begin to see themselves as part of a larger sociotechnical system. Finally, as medicine becomes increasingly tech-laden, it’s important for clinicians to see how material artifacts (including algorithms) connect individuals to structures. This will help to undermine oversimplified narratives according to which objective tools and technologies can correct for the bias and subjectivity of flawed human beings. (shrink)

We present an elementary system of axioms for the geometry of Minkowski spacetime. It strikes a balance between a simple and streamlined set of axioms and the attempt to give a direct formalization in first-order logic of the standard account of Minkowski spacetime in [Maudlin 2012] and [Malament, unpublished]. It is intended for future use in the formalization of physical theories in Minkowski spacetime. The choice of primitives is in the spirit of [Tarski 1959]: a predicate of betwenness and a (...) four place predicate to compare the square of the relativistic intervals. Minkowski spacetime is described as a four dimensional ‘vector space’ that can be decomposed everywhere into a spacelike hyperplane - which obeys the Euclidean axioms in [Tarski and Givant, 1999] - and an orthogonal timelike line. The length of other ‘vectors’ are calculated according to Pythagora’s theorem. We conclude with a Representation Theorem relating models of our system that satisfy second order continuity to the mathematical structure called ‘Minkowski spacetime’ in physics textbooks. (shrink)

The present yearbook (which is the fourth in the series) is subtitled Trends & Cycles. It is devoted to cyclical and trend dynamics in society and nature; special attention is paid to economic and demographic aspects, in particular to the mathematical modeling of the Malthusian and post-Malthusian traps' dynamics. An increasingly important role is played by new directions in historical research that study long-term dynamic processes and quantitative changes. This kind of history can hardly develop without the application of mathematical (...) methods. There is a tendency to study history as a system of various processes, within which one can detect waves and cycles of different lengths – from a few years to several centuries, or even millennia. The contributions to this yearbook present a qualitative and quantitative analysis of global historical, political, economic and demographic processes, as well as their mathematical models. This issue of the yearbook consists of three main sections: (I) Long-Term Trends in Nature and Society; (II) Cyclical Processes in Pre-industrial Societies; (III) Contemporary History and Processes. We hope that this issue of the yearbook will be interesting and useful both for historians and mathematicians, as well as for all those dealing with various social and natural sciences. (shrink)

In the chapter of Difference and Repetition entitled ‘Ideas and the synthesis of difference,’ Deleuze mobilizes mathematics to develop a ‘calculus of problems’ that is based on the mathematical philosophy of Albert Lautman. Deleuze explicates this process by referring to the operation of certain conceptual couples in the field of contemporary mathematics: most notably the continuous and the discontinuous, the infinite and the finite, and the global and the local. The two mathematical theories that Deleuze draws upon for this purpose (...) are the differential calculus and the theory of dynamical systems, and Galois’ theory of polynomial equations. For the purposes of this paper I will only treat the first of these, which is based on the idea that the singularities of vector fields determine the local trajectories of solution curves, or their ‘topological behaviour’. These singularities can be described in terms of the given mathematical problematic, that is for example, how to solve two divergent series in the same field, and in terms of the solutions, as the trajectories of the solution curves to the problem. What actually counts as a solution to a problem is determined by the specific characteristics of the problem itself, typically by the singularities of this problem and the way in which they are distributed in a system. Deleuze understands the differential calculus essentially as a ‘calculus of problems’, and the theory of dynamical systems as the qualitative and topological theory of problems, which, when connected together, are determinative of the complex logic of different/ciation. (DR 209). Deleuze develops the concept of a problematic idea from the differential calculus, and following Lautman considers the concept of genesis in mathematics to ‘play the role of model ... with respect to all other domains of incarnation’. While Lautman explicated the philosophical logic of the actualization of ideas within the framework of mathematics, Deleuze (along with Guattari) follows Lautman’s suggestion and explicates the operation of this logic within the framework of a multiplicity of domains, including for example philosophy, science and art in What is Philosophy?, and the variety of domains which characterise the plateaus in A Thousand Plateaus. While for Lautman, a mathematical problem is resolved by the development of a new mathematical theory, for Deleuze, it is the construction of a concept that offers a solution to a philosophical problem; even if this newly constructed concept is characteristic of, or modelled on the new mathematical theory. (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)

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)

A new AI system, called AlphaGeometry, trained under synthetic data has demonstrated the ability to solve geometric problems at the International Olympiad level. This essay considers the fact that human abilities to learn and do math as well as many other tasks are increasingly augmented with AI. Clearly, smart technologies like AlphaGeometry are redefining a number of concepts and institutions such as learning, schools, education, teacher-student relationships, creativity, etc, which are so fundamental for what we’ve thought of as modern society, (...) economy, and culture. What are we preparing for in mathematics education in the face of the possibility of the continued emergence of disruptive technologies, signaling the beginning of the end, if a new reality of mathematics is not taken into account? (shrink)

In this article, I define a cultural epistemology as a set of socially reinforced assumptions about how knowledge and truth are produced. Unlike a philosophical epistemology, a cultural epistemology is largely the product of culture and largely invisible. As products of culture, cultural epistemology are relatively unquestioned and, in many cases, philosophically unsophisticated. There are three common types of cultural epistemologies, influenced by who holds power in a given society: an epistemological monarchy, an epistemological oligarchy and (...) an epistemological democracy. A given cultural epistemology subsequently influences the legitimacy of culture and government itself. I argue argue that Americans tend to hold an "epistemological democracy" with two distinct facets: a trust in consensus, linked to living in a democratic republic, and a trust in their own self-interest, linked to market economics and capitalism more generally. These two facets combine, interact, and even oppose each other to legitimize and challenge American culture and its political and economic systems. (shrink)

The main argument of this paper is that the legal regulation of lobbying is an important factor for disciplining/curbing the undue (illicit) influence of different interest groups on the political-making process, especially in countries with post-communist and nonconsolidated democracies such as Albania. In three decades of political and economic transition from a one-party communist system to a democratic one and towards a market economy, the democratization of Albania has faced various problems, which have often led to a loss of public (...) confidence in the political class and apathy of citizens towards the political system. In many cases, this has come as a result of the perception or even the disclosure by the media and the public of corruption scandals, political clientelism, or undue influences in the decision-making processes in Albania. Surely, it can be said that political scandals of trading or exercising illicit influences on public officials can affect, as numerous cases have shown, every democratic political system in the world. However, they are more likely to occur in new democracies (post-communist) countries that face weak state structures and a legal environment that is not yet well consolidated and where a culture of informality exists alongside written rules and laws. For this purpose, that of disciplining and controlling the influences that specific interests exert on the decision-making process of governments, legislatures, or other regulatory agencies, a good part of European countries have considered undertaking legal regulatory initiatives for lobbying activity in their environments. (shrink)

The term “Complex Systems Biology” was introduced a few years ago [Kaneko, 2006] and, although not yet of widespread use, it seems particularly well suited to indicate an approach to biology which is well rooted in complex systems science. Although broad generalizations are always dangerous, it is safe to state that mainstream biology has been largely dominated by a gene-centric view in the last decades, due to the success of molecular biology. So the one gene - one trait approch, which (...) has often proved to be effective, has been extended to cover even complex traits. This simplifying view has been appropriately criticized, and the movement called systems biology has taken off. Systems biology [Noble, 2006] emphasizes the presence of several feedback loops in biological systems, which severely limit the range of validity of explanations based upon linear causal chains (e.g. gene → behaviour). Mathematical modelling is one the favourite tools of systems biologists to analyze the possible effects of competing negative and positive feedback loops which can be observed at several levels (from molecules to organelles, cells, tissues, organs, organisms, ecosystems). Systems biology is by now a well-established field, as it can be inferred by the rapid growth in number of conferences and journals devoted to it, as well as by the existence of several grants and funded projects.Systems biology is mainly focused upon the description of specific biological items, like for example specific organisms, or specific organs in a class of animals, or specific genetic-metabolic circuits. It therefore leaves open the issue of the search for general principles of biological organization, which apply to all living beings or to at least to broad classes. We know indeed that there are some principles of this kind, biological evolution being the most famous one. The theory of cellular organization also qualifies as a general principle. But the main focus of biological research has been that of studying specific cases, with some reluctance to accept (and perhaps a limited interest for) broad generalizations. This may however change, and this is indeed the challenge of complex systems biology: looking for general principles in biological systems, in the spirit of complex systems science which searches for similar features and behaviours in various kinds of systems. The hope to find such general principles appears well founded, and I will show in Section 2 that there are indeed data which provide support to this claim. Besides data, there are also general ideas and models concerning the way in which biological systems work. The strategy, in this case, is that of introducing simplified models of biological organisms or processes, and to look for their generic properties: this term, borrowed from statistical physics, is used for those properties which are shared by a wide class of systems. In order to model these properties, the most effective approach has been so far that of using ensembles of systems, where each member can be different from another one, and to look for those properties which are widespread. This approach was introduced many years ago [Kauffman, 1971] in modelling gene regulatory networks. At that time one had very few information about the way in which the expression of a given gene affects that of other genes, apart from the fact that this influence is real and can be studied in few selected cases (like e.g. the lactose metabolism in E. coli). Today, after many years of triumphs of molecular biology, much more has been discovered, however the possibility of describing a complete map of gene-gene interactions in a moderately complex organism is still out of reach. Therefore the goal of fully describing a network of interacting genes in a real organism could not be (and still cannot be) achieved. But a different approach has proven very fruitful, that of asking what are the typical properties of such a set of interacting genes. Making some plausible hypotheses and introducing some simplifying assumptions, Kauffman was able to address some important problems. In particular, he drew attention to the fact that a dynamical system of interacting genes displays selforganizing properties which explain some key aspects of life, most notably the existence of a limited number of cellular types in every multicellular organism (these numbers are of the order of a few hundreds, while the number of theoretically possible types, absent interactions, would be much much larger than the number of protons in the universe). In section 3 I will describe the ensemble based approach in the context of gene regulatory networks, and I will show that it can describe some important experimental data. Finally, in section 4 I will discuss some methodological aspects. (shrink)

This article explores the cultural contexts in which three-dimensional imaging has been developed, disseminated and used. It surveys the diverse technologies and intellectual domains that have contributed to spatial imaging, and argues that it is an important example of an interdisciplinary subject. Over the past century-and-a-half, specialists from distinct fields have devised explanations and systems for the experience of 3-D imagery. Successive audiences have found these visual experiences compelling, adapting quickly to new technical possibilities and seeking new ones. These (...) complementary interests, and their distinct perspectives, have co-evolved in lock-step. A driver for this evolution is visual culture, which has grown to value and demand the spectacular. As a result, professional and popular engagements with 3-D have had periods of both popularity and indifference, and cultural consensus has proven to be ephemeral. (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)

Part of education as interactive exercise is related to a community of practitioners, a dialogue based philosophy of morals which supposes ethical normative characteristics of the discourse. This normative layer can be interpreted either in relation to the lifeworld, i. e. to the understanding of the good life. Alternatively, it can be realized in relation to some cultural rights, since a mutual recognition based ethics, aiming at highlighting culture as necessary feature of human dignity, can explain an ultimate goal (...) of higher education as global and universal education. Since the whole set of human rights should be seen as an indivisible system of basic limits to individual and collective freedom, a right based approach would be the other main perspective, certainly relevant in the context of the African continent, as it is worldwide. Furthermore a right based understanding is a much ignored aspect of human rights, although intimately related to basic interests of the higher education system from either the point of view of the national education systems, or as private universities and it is also related to non-governmental organisations understanding of the general aim of higher education development, where international organizations could help in the implementation of these cultural rights based good practices. In the first section we first develop briefly a normative ethical model of education based on the transformative model of the ethics of discourse compared to other possible classical models based on merit, then we will present cultural rights, reminding us some aspects of cultural rights related to higher education, and address the relevance for the African context of a contextual reflection on these rights. (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)

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)

The phenomenon of corruption is a cancer that affects our country and that it is necessary to eradicate; This dilutes the opportunities for economic and social development, privileging the single conjunction of particular interests, political actors in non-legal agreements for their own benefit, which lead to acts of corruption. Recent studies indicate that the level of corruption present in a political system is directly related to the type of institutional structure that defines it (Boehm and Lambsdorff, 2009), as well (...) as the ineffectiveness of the control organisms (Casar, 2015; Cárdenas, 2010, Rojas, 2010, Carbonell, 2009, Restrepo, 2004), which requires citizen action to combat corruption (Sandoval, 2010, Villanueva, 2006). This work, focuses our attention on the federal public administration, presenting as a proposal to empower the citizen action in the fight against corruption and in the National Anticorruption System; the figure of Whistleblowers or generator of citizen alert, based on two fundamental principles: i) recognizing the citizen's obligation to report acts of corruption and ii) the granting by the authority of witness protection. These two actions will result in two important results: i) Consolidate the citizen's complaint to inform society about acts of corruption and ii) and the exercise of freedom of information so that society is able to be informed about acts of corruption. These actions will allow promoting and consolidating a culture of reporting acts of corruption that may constitute a crime as a fundamental pillar in the National Anticorruption System in Mexico. (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)

Disciplinary issues -- Field studies -- Appendix: Theory of law : legal ethnography, or, the theoretical fruits of the inquiries into folkways. /// Reedition of papers in English spanning from 1995 to 2008 /// DISCIPLINARY ISSUES -- LAW AS CULTURE? [2002] 9–14 // TRENDS IN COMPARATIVE LEGAL STUDIES [2002] 15–17 // COMPARATIVE LEGAL CULTURES: ATTEMPTS AT CONCEPTUALISATION [1997] 19–28: 1. Legal Culture in a Cultural-anthropological Approach 19 / 2. Legal Culture in a Sociological Approach 21 / 3. Timely Issues (...) of Central and Eastern Europe 24 // COMPARATIVE LEGAL CULTURES? [2001] 29–48: 1. Legal Comparativism Challenged 29 / 2. Comparative Legal Cultures versus Comparative Law 34 / 3. Contrasting Fields 40 [a) The Historical Understanding of Socialist Law 42 / b) Convergence of Civil Law and Common Law 44] 4. Concluding Remarks 46 // THEATRUM LEGALE MUNDI: ON LEGAL SYSTEMS CLASSIFIED [2005] 49–75: 1. Preliminaries 49 / 2. Proposals 50 / 3. Impossible Taxonomy, or the Moment of Practicality in Legal Mapping 69 / 4. Diversity as a Fundamental Quality of Human Existence 74 // LEGAL TRADITIONS? IN SEARCH FOR FAMILIES AND CULTURES IN LAW [2004] 77–97: 1. Comparative Law and the Comparative Study of Legal Traditions 78 / 2. ‘System’, ‘Family’, ‘Culture’, and ‘Tradition’ in the Classification of Law 80 / 3. Different Traditions, Differing Ways of Thinking 85 / 4. Different Expectations, Differings Institutionalisations in Law 88 / 5. Different “Rationalities”, Differing “Logics” 92 / 6. Mentality in Foundation of the Law 94 / 7. Defining a Subject for Theoretical Research in Law 96 // SOMETHING NEW, SOMETHING OLD IN THE EUROPEAN IDENTITY OF LAW? [1995] 99–102 --- FIELD STUDIES -- MEETING POINTS BETWEEN THE TRADITIONS OF ENGLISH–AMERICAN COMMON LAW AND CONTINENTAL-FRENCH CIVIL LAW: DEVELOPMENTS AND EXPERIENCE OF POSTMODERNITY IN CANADA [2002] 105–130: I. Canadian Law in General 105 / II. Canadian Legal Developments in Particular [1. The Transformation of the Role of Precedents 112 / 2. The Transformation of Law-application into a Collective, Multicultural and Multifactorial Search for a Solution 116 / 3. Practical Trends of Dissolving the Law’s Positivity 120 / 4. New Prerogatives Acquired by Courts 125 {a) Unfolding the Statutory Provisons in Principles 126 / b) Constitutionalisation of Issues 127 / c) The Supreme Court as the Nation’s Supreme Moral Authority 129}] // MAN ELEVATING HIMSELF? DILEMMAS OF RATIONALITY IN OUR AGE [2000] 131–163: I. Reason and its Adventures 1. Progress and Advance Questioned 131 / 2. The Human Search for Safety Objectified 133 / 3. Knowledge Separated from Wisdom 135 / 4. Pure Intellectuality thereby Born 137 / II. The Will-Element Formalised in Law 5. Mere Voluntas in the Foundation of Legal Positivism 141 / 6. Formalism with Operations Fragmented 145 / III. The State of America Exemplified 7. “Slouching into Gomorrah” 147 / IV. Consequences 8. Utopianism-cum-Voluntarism 154 / 9. With Logic in Posterior Control of Human Formulations Only 159 / V. Perspectives 10. And a Final Resolution Dreamed about 161 // RULE OF LAW? MANIA OF LAW? ON THE BOUNDARY BETWEEN RATIONALITY AND ANARCHY IN AMERICA [2002] 165–180: {Transformation of American Law and Legal Mentality 165 / With Repercussions on the Underlying Ethos 168 / Legislation through Processualisation 170 / With Hyperrationalism Added 172 / Example: Finding Lost Property 172 / Practicalness Veiled by Verbal Magic 173 / Ending in Jurispathy 175 / Transubstantiating the Self-interest of the Legal Profession 178 / Post-modernity, Substituting for Primitiveness 178} // TRANSFERS OF LAW: A CONCEPTUAL ANALYSIS [2003] 181–207: 1. Terms 182 / 2. Technicality 190 / 3. Contrasts in Transfers of Law 200 {Contrasts 200 / Criticisms 202 / Alternatives205} 4. Conclusions 206 // THE DANGERS FOR THE SELF OF BEING SELF-CENTRED: ON STANDARDS AND VALUES [2002] 209–212 --- APPENDIX -- THEORY OF LAW – LEGAL ETHNOGRAPHY, OR THE THEORETICAL FRUITS OF THE INQUIRIES INTO FOLKWAYS [2008] 213–234 1. Encounters 213 / 2. Disciplines 218 / 3. The Lawyerly Interest 223 / 4. Law and/or Laws 226 / 5. Conclusion 233 --- Index of Subjects 235 / Index of Normative Materials 242 / Index 244 . (shrink)

In computational complexity theory, decision problems are divided into complexity classes based on the amount of computational resources it takes for algorithms to solve them. In theoretical computer science, it is commonly accepted that only functions for solving problems in the complexity class P, solvable by a deterministic Turing machine in polynomial time, are considered to be tractable. In cognitive science and philosophy, this tractability result has been used to argue that only functions in P can feasibly work as computational (...) models of human cognitive capacities. One interesting area of computational complexity theory is descriptive complexity, which connects the expressive strength of systems of logic with the computational complexity classes. In descriptive complexity theory, it is established that only first-order systems are connected to P, or one of its subclasses. Consequently, second-order systems of logic are considered to be computationally intractable, and may therefore seem to be unfit to model human cognitive capacities. This would be problematic when we think of the role of logic as the foundations of mathematics. In order to express many important mathematical concepts and systematically prove theorems involving them, we need to have a system of logic stronger than classical first-order logic. But if such a system is considered to be intractable, it means that the logical foundation of mathematics can be prohibitively complex for human cognition. In this paper I will argue, however, that this problem is the result of an unjustified direct use of computational complexity classes in cognitive modelling. Placing my account in the recent literature on the topic, I argue that the problem can be solved by considering computational complexity for humanly relevant problem solving algorithms and input sizes. (shrink)

Computer assisted theorem proving is an increasingly important part of mathematical methodology, as well as a long-standing topic in artificial intelligence (AI) research. However, the current generation of theorem proving software have limited functioning in terms of providing new proofs. Importantly, they are not able to discriminate interesting theorems and proofs from trivial ones. In order for computers to develop further in theorem proving, there would need to be a radical change in how the software functions. Recently, machine learning results (...) in solving mathematical tasks have shown early promise that deep artificial neural networks could learn symbolic mathematical processing. In this paper, I analyze the theoretical prospects of such neural networks in proving mathematical theorems. In particular, I focus on the question how such AI systems could be incorporated in practice to theorem proving and what consequences that could have. In the most optimistic scenario, this includes the possibility of autonomous automated theorem provers (AATP). Here I discuss whether such AI systems could, or should, become accepted as active agents in mathematical communities. (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)

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 is Wittgenstein´s least interesting book, being only random notes dealing with art, music, religion and other areas of culture, taken from his notebooks over the course of his life. But W is never dull and it's a measure of the awe in which he is held that this book was even published. I can´t imagine publishing such a book by anyone else,-certainly no philosopher. Those interested in W should go to nearly any of the other 20,000 odd pages of (...) his works (but NOT the Tractatus!)-but those with little acquaintance be forewarned, though W may seem a shallow tepid pool, if you jump in you may never stop swimming. Those wishing a comprehensive up to date account of Wittgenstein, Searle and their analysis of behavior from the modern two systems view may consult my article The Logical Structure of Philosophy, Psychology, Mind and Language as Revealed in Wittgenstein and Searle (2016). Those interested in all my writings in their most recent versions may download from this site my e-book ‘Philosophy, Human Nature and the Collapse of Civilization Michael Starks (2016)- Articles and Reviews 2006-2016’ by Michael Starks First Ed. 662p (2016). All of my papers and books have now been published in revised versions both in ebooks and in printed books. Talking Monkeys: Philosophy, Psychology, Science, Religion and Politics on a Doomed Planet - Articles and Reviews 2006-2017 (2017) The Logical Structure of Philosophy, Psychology, Mind and Language in Ludwig Wittgenstein and John Searle--Articles and Reviews 2006-2016 (2017) Suicidal Utopian Delusions in the 21st century: Philosophy, Human Nature and the Collapse of Civilization - Articles and Reviews 2006-2017 (2017) . (shrink)

This article addresses the question of the coherence of enactivism as a research perspective by making a case study of enactivism in mathematics education research. Main theoretical directions in mathematics education are reviewed and the history of adoption of concepts from enactivism is described. It is concluded that enactivism offers a ‘grand theory’ that can be brought to bear on most of the phenomena of interest in mathematics education research, and so it provides a sufficient theoretical framework. It has particular (...) strength in describing interactions between cognitive systems, including human beings, human conversations and larger human social systems. Some apparent incoherencies of enactivism in mathematics education and in other fields come from the adoption of parts of enactivism that are then grafted onto incompatible theories. However, another significant source of incoherence is the inadequacy of Maturana’s definition of a social system and the lack of a generally agreed upon alternative. (shrink)

Let us start by some general definitions of the concept of complexity. We take a complex system to be one composed by a large number of parts, and whose properties are not fully explained by an understanding of its components parts. Studies of complex systems recognized the importance of “wholeness”, defined as problems of organization (and of regulation), phenomena non resolvable into local events, dynamics interactions in the difference of behaviour of parts when isolated or in higher configuration, etc., in (...) short, systems of various orders (or levels) not understandable by investigation of their respective parts in isolation. In a complex system it is essential to distinguish between ‘global’ and ‘local’ properties. Theoretical physicists in the last two decades have discovered that the collective behaviour of a macro-system, i.e. a system composed of many objects, does not change qualitatively when the behaviour of single components are modified slightly. Conversely, it has been also found that the behaviour of single components does change when the overall behaviour of the system is modified. There are many universal classes which describe the collective behaviour of the system, and each class has its own characteristics; the universal classes do not change when we perturb the system. The most interesting and rewarding work consists in finding these universal classes and in spelling out their properties. This conception has been followed in studies done in the last twenty years on second order phase transitions. The objective, which has been mostly achieved, was to classify all possible types of phase transitions in different universality classes and to compute the parameters that control the behaviour of the system near the transition (or critical or bifurcation) point as a function of the universality class. This point of view is not very different from the one expressed by Thom in the introduction of Structural Stability and Morphogenesis (1975). It differs from Thom’s program because there is no a priori idea of the mathematical framework which should be used. Indeed Thom considers only a restricted class of models (ordinary differential equations in low dimensional spaces) while we do not have any prejudice regarding which models should be accepted. One of the most interesting and surprising results obtained by studying complex systems is the possibility of classifying the configurations of the system taxonomically. It is well-known that a well founded taxonomy is possible only if the objects we want to classify have some unique properties, i.e. species may be introduced in an objective way only if it is impossible to go continuously from one specie to another; in a more mathematical language, we say that objects must have the property of ultrametricity. More precisely, it was discovered that there are conditions under which a class of complex systems may only exist in configurations that have the ultrametricity property and consequently they can be classified in a hierarchical way. Indeed, it has been found that only this ultrametricity property is shared by the near-optimal solutions of many optimization problems of complex functions, i.e. corrugated landscapes in Kauffman’s language. These results are derived from the study of spin glass model, but they have wider implications. It is possible that the kind of structures that arise in these cases is present in many other apparently unrelated problems. Before to go on with our considerations, we have to pick in mind two main complementary ideas about complexity. (i) According to the prevalent and usual point of view, the essence of complex systems lies in the emergence of complex structures from the non-linear interaction of many simple elements that obey simple rules. Typically, these rules consist of 0–1 alternatives selected in response to the input received, as in many prototypes like cellular automata, Boolean networks, spin systems, etc. Quite intricate patterns and structures can occur in such systems. However, what can be also said is that these are toy systems, and the systems occurring in reality rather consist of elements that individually are quite complex themselves. (ii) So, this bring a new aspect that seems essential and indispensable to the emergence and functioning of complex systems, namely the coordination of individual agents or elements that themselves are complex at their own scale of operation. This coordination dramatically reduces the degree of freedom of those participating agents. Even the constituents of molecules, i.e. the atoms, are rather complicated conglomerations of subatomic particles, perhaps ultimately excitations of patterns of superstrings. Genes, the elementary biochemical coding units, are very complex macromolecular strings, as are the metabolic units, the proteins. Neurons, the basic elements of cognitive networks, themselves are cells. In those mentioned and in other complex systems, it is an important feature that the potential complexity of the behaviour of the individual agents gets dramatically simplified through the global interactions within the system. The individual degrees of freedom are drastically reduced, or, in a more formal terminology, the factual space of the system is much smaller than the product of the state space of the individual elements. That is one key aspect. The other one is that on this basis, that is utilizing the coordination between the activities of its members, the system then becomes able to develop and express a coherent structure at a higher level, that is, an emergent behaviour (and emergent properties) that transcends what each element is individually capable of. (shrink)

The work is an attempt to transfer a structure from Euclidean plane (pure geometrical) under the physical observation limit (resolving power) to a physical space (observable space). The transformation from the mathematical space to physical space passes through the observation condition. The mathematical modelling is adopted. The project is based on two stapes: (1) Looking for a simple mathematical model satisfies the definition of Euclidian plane; (2)That model is examined against three observation resolution conditions (resolved, unresolved and partially resolved). The (...) simplest mechanical model satisfies the definition of Euclidian plane is a planetary gear. The interesting examination of the mechanical model is that is under partial resolution. That examination shows analogous equation for Euler’s formula. The derived complex formula contains the resolved (observable) quantities of the mechanical system and satisfies the linear wave equation. The interpretation of this complex formula is: it is a function related to the position vector of a point in the small wheel of the partially resolved planetary gear system. The function is in terms of the observable quantities only. The work shows the possibility of transformation from real to complex space. The work is purely classical but the result of the partial resolution shows a function similar to the Quantum mechanics wave function. (shrink)

Effective stakeholder engagement and inclusive governance are essential for effective and equitable ocean management. However, few cross-national studies have been conducted to examine how stakeholders’ economic and cultural benefit perceptions influence their support level for policies focused on ocean preservation. The current study aims to fill this gap by employing the Bayesian Mindsponge Framework (BMF) analytics on a dataset of 709 stakeholders from 42 countries, a part of the MaCoBioS project funded by the European Commission H2020. We found that (...) economic and cultural benefit perceptions are generally negatively associated with the policy support level. Regarding economic aspects, stakeholders considering transportation and shipping, renewable energy generation, and oil and gas provision as the most crucial benefits their countries’ oceans provide tend to obtain less support for policies focusing on ocean preservation. Meanwhile, for cultural aspects, perceiving recreation and tourism, aesthetic pleasure, mental health and well-being support, and sense of identity provision as the most important benefits provided by the country’s ocean are negatively associated with the policy support level. The perceived economic, cultural, and environmental tradeoffs when supporting policies focused on ocean preservation were discussed. Recommendations for improving the effective management of multi-use marine space are also provided to reduce the perceived competing interests among stakeholders. (shrink)

This study sought to examine the factors affecting the Science, Technology, Engineering and Mathematics (STEM) students’ Mathematics performance in a modular distance learning at Notre Dame Village National High School (NDVNHS). In particular, the researcher was interested to determine if these factors had a significant effect on the students’ Pre-Calculus and General Mathematics performance considering the number of hours spent in modular learning. The period covered by the study was during the first semester of the school year 2020-2021. The respondents (...) were all 67 Grade 11 STEM students of NDVNHS. A quantitative research design was utilized particularly using Multivariate Analysis of Covariance (MANCOVA). The findings of the study revealed that majority of the STEM students had a good performance in their Mathematics subjects for the first semester. Also, the factors specifically type of motivation (intrinsic or extrinsic) and support system (parents, siblings, relatives, friends, or classmates) had statistically significant effect on their mathematics performance in the new normal considering the amount of time they spent in learning using modules. Moreover, there were statistically significant differences in both Pre-Calculus and General Mathematics performances between the type of motivation and support system when adjusted for the number of hours spent in modular learning. Based on the findings, the study concluded that the students’ motivation and support system can greatly affect their mathematics performance when controlling for the allocated time in modular learning. Especially in Pre-Calculus and General Mathematics, motivation and support system are important factors in learning using modules. In the new normal education, the students should increase their level of motivation as well as exposure in self-learning and be given full support towards the processes in the modular approach of distance learning. (shrink)

Johannes Müller von Königsberg (1436-1476), better known as Regiomontanus, is widely considered as the most influential astronomer and mathematician of 15th-century Europe. He was active as an astrologer and deemed astrology to be the queen of mathematical sciences. Despite this, Regiomontanus's astrological activity has yet to be fully explored. A brief examination of Regiomontanus's manuscripts shows that his astrological interests were accompanied by interests in the arts and in methods of prognostication. This article studies an unconventional astrological-chiromantical text, (...) whose relevance is threefold: a) it sheds new light on Regiomontanus's astrological interests; b) it enriches our knowledge of Regiomontanus's efforts to learn and understand Greek-Regiomontanus transcribed it into his own manuscript during his sojourn in Italy from 1460-1467; and c) it is the sole extant text in the Greek tradition that provides a system for prognostication from the study of a person's hand, the parts of which are considered as being under the domain of planets. The article provides an English translation of Regiomontanus's transcription, alongside a brief commentary, and studies the intellectual and historical context of that production through manuscript analysis. (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)

Our starting point is the question ‘What is mass’, what in particular enables mass to constitute duration: so that mass can be regarded as moving as well as at rest (the kinematic principle of relativity). In a thought experiment, this question is attacked here not from the perspective of mass itself, but from that of a standing light wave. In this model, mass-analogous structures can be re- constructed that can be in relative motion to each other. The (empirically known) constancy (...) of the speed of light in every reference system is not as- sumed here. However, it can be shown that the speed of light is identical in all systems constituted by mass-analogous structures that move uniformly relative to each other and that the speed of light moreover is the limiting speed of mo- tions. This indepence of the motion of light from the system of reference, this character of absoluteness, and the relativity of mass motions thus prove to be contrary but inextricably linked moments of the kinematic principle of relativi- ty: an interesting perspective concerning a philosophy of relativity theory. - The mathematical relationships are explained in more detail in the appendix. (shrink)

In this work we study dimensional theoretical properties of some a±ne dynamical systems. By dimensional theoretical properties we mean Hausdor® dimension and box- counting dimension of invariant sets and ergodic measures on theses sets. Especially we are interested in two problems. First we ask whether the Hausdor® and box- counting dimension of invariant sets coincide. Second we ask whether there exists an ergodic measure of full Hausdor® dimension on these invariant sets. If this is not the case we ask the (...) question, whether at least the variational principle for Haus- dor® dimension holds, which means that there is a sequence of ergodic measures such that their Hausdor® dimension approximates the Hausdor® dimension of the invariant set. It seems to be well accepted by experts that these questions are of great importance in developing a dimension theory of dynamical systems (see the book of Pesin about dimension theory of dynamical systems [PE2]). Dimensional theoretical properties of conformal dynamical systems are fairly well understood today. For example there are general theorems about conformal repellers and hyperbolic sets for conformal di®eomorphisms (see chapter 7 of [PE2]). On the other hand the existence of two di®erent rates of expansion or contraction forces problems that are not captured by a general theory this days. At this stage of de- velopment of the dimension theory of dynamical systems it seems natural to study non conformal examples. This is the ¯rst step to understand the mechanisms that determine dimensional theoretical properties of non conformal dynamical systems. A±ne dynamical systems represent simple examples of non conformal systems. They are easy to de¯ne, but studying their dimensional theoretical properties does never- theless provide challenging mathematical problems and exemplify interesting phe- nomena. We consider here a special class of self-a±ne repellers in dimension two, depending on four parameters (see 2.1.). Furthermore we study a class of attractors of piecewise a±ne maps in dimension three depending on four parameters as well. The last object of our work are projections of these maps that are known as gener- alized Baker's transformations (see 2.2.). The contents of our work is the following: In chapter two we give an overview about some main results in the area of di- mension theory of a±ne dynamical systems and de¯ne the systems we study in this work. We will explain, what is known about the dimensional theoretical properties of these systems and describe what our new results are. In chapter three we then apply symbolic dynamics to our systems. We will introduce explicit shift codings 4 and ¯nd representations of all ergodic measures for our systems using these codings. From chapter four to chapter eight we study dimensional theoretical properties, which our systems generally or generically have. In chapter four we will prove a formula for the box-counting dimension of the repellers and the attractors (see the- orem 4.1.). Then in chapter ¯ve we apply general dimensional theoretical results for ergodic measures found by Ledrappier and Young [LY] and Barreira, Schmeling and Pesin [BPS] to our systems. These results relate the dimension of ergodic measures to metric entropy and Lyapunov exponents. Using this approach we will be able to reduce questions about the dimension of ergodic measures in our context to ques- tions about certain overlapping and especially overlapping self-similar measures on the line. These overlapping self-similar measures are studied in chapter six. Our main theorem extends a result of Peres and Solomyak [PS2] concerning the absolute continuity resp. singularity of symmetric self-similar measures to asymmetric ones (see theorem 6.1.3.). In chapter seven we bring our results together. We prove that we generically (in the sense of Lebesgue measure on a part of the parameter space) have the iden- tity of box-counting and Hausdor® dimension for the repellers and the attractors. (see theorem 7.1.1. and corollary 7.1.2.). This result suggest that one can expect that the identity of box-counting dimension and Hausdor® dimension holds at least generically in some natural classes of non conformal dynamical systems. Furthermore we will see in chapter seven that there generically exists an ergodic measure of full Hausdor® dimension for the repellers. On the other hand the vari- ational principle for Hausdor® dimension is not generic for the attractors. It holds only if we assume a certain symmetry (see theorem 7.1.1.). For generalized Baker's transformations we will ¯nd a part of the parameter space where there generically is an ergodic measure of full dimension and a part where the variational principle for Hausdor® dimension does not hold (see theorem 7.1.3.). Roughly speaking the reason why the variational principle does not hold here is, that if there exists both a stable and an unstable direction one can not generically maximize the dimension in the stable and in the unstable direction at the same time. In an other setting this phenomenon was observed before by Manning and McCluskey [MM]. In chapter eight we extend some results of the last section to invariant sets that correspond to special Markov chains instead of full shifts (see theorem 8.1.1.). In the last two chapters of our work we are interested in number theoretical excep- tions to our generic results. The starting point of our considerations in section nine are results of ErdÄos [ER1] and Alexander and Yorke [AY] that establish singularity and a decrease of dimension for in¯nite convolved Bernoulli measures under special conditions. Using a generalized notion of the Garsia entropy ([GA1/2]) we are able 5 to understand the consequences of number theoretical peculiarities in broader class of overlapping measures (see theorem 9.1.1.). In chapter ten we then analyze number theoretical peculiarities in the context of our dynamical systems. We restrict our attention to a symmetric situation where we generically have the existence of a Bernoulli measure of full dimension and the identity of Hausdor® and box-counting dimension for all of our systems. In the ¯rst section of chapter ten we ¯nd parameter values such that the variational principle for Hausdor® dimension does not hold for the attractors and for the Fat Baker's transformations (see theorem 10.1.1.). These are the ¯rst known examples of dynamical systems for which the variational principle for Hausdor® dimension does not hold because of number theoretical peculiarities of parameter values. For the repellers we have been able to show that under certain number theoretical conditions there is at least no Bernoulli measure of full Hausdor® dimension; the question if the variational principle for Hausdor® dimension holds remains open in this situation. In the second section of chapter ten we will show that the identity for Hausdor® and box-counting dimension can drops because there are number theoretical pecu- liarities. In the context of Weierstrass-like functions this phenomenon was observed by Przytycki and Urbanski [PU]. Our theorem extends this result to a larger class of sets, invariant under dynamical systems (see theorem 10.2.1). At the end of this work the reader will ¯nd two appendices, a list of notations and the list of references. In appendix A we introduce the notions of dimension we use in this work and collect some general facts in dimension theory. In appendix B we state the facts about Pisot-Vijayarghavan number, we need in our analysis of number theoretical peculiarities. The list of notations contains general notations and a table with a summary of notations we use to describe the dynamical systems that we study. Acknowledgments I wish to thank my supervisor JÄorg Schmeling for a lot of valuable discussion and all his help. Also thanks to Luis Barreira for his great hospitality in Lisboa and many interesting comments. This work was done while I was supported by "Promotionstipendium gem. NaFÄoG der Freien UniversitÄat Berlin". (shrink)

Years ago, when I was an undergraduate math major at the University of Wyoming, I came across an interesting book in our library. It was a book of counterexamples t o propositions in real analysis (the mathematics of the real numbers). Mathematicians work more or less like the rest of us. They consider propositions. If one seems to them to be plausibly true, then they set about to prove it, to establish the proposition as a theorem. Instead o f setting (...) out to prove propositions, the psychologists, neuroscientists, and other empirical types among us, set out to show that a proposition is supported by the data, and that it is the best such proposition so supported. The philosophers among us, when they are not causing trouble by arguing that AI is a dead end or that cognitive science can get along without representations, work pretty much like the mathematicians: we set out to prove certain propositions true on the basis of logic, first principles, plausible assumptions, and others' data. But, back to the book of real analysis counterexamples. If some mathematician happened t o think that some proposition about continuity, say, was plausibly true, he or she would then set out to prove it. If the proposition was in fact not a theorem, then a lot of precious time would be wasted trying to prove it. Wouldn't it be great to have a book that listed plausibly true propositions that were in fact not true, and listed with each such proposition a counterexample to it? Of course it would. (shrink)

This fifth volume on Advances and Applications of DSmT for Information Fusion collects theoretical and applied contributions of researchers working in different fields of applications and in mathematics, and is available in open-access. The collected contributions of this volume have either been published or presented after disseminating the fourth volume in 2015 in international conferences, seminars, workshops and journals, or they are new. The contributions of each part of this volume are chronologically ordered. First Part of this book presents some (...) theoretical advances on DSmT, dealing mainly with modified Proportional Conflict Redistribution Rules (PCR) of combination with degree of intersection, coarsening techniques, interval calculus for PCR thanks to set inversion via interval analysis (SIVIA), rough set classifiers, canonical decomposition of dichotomous belief functions, fast PCR fusion, fast inter-criteria analysis with PCR, and improved PCR5 and PCR6 rules preserving the (quasi-)neutrality of (quasi-)vacuous belief assignment in the fusion of sources of evidence with their Matlab codes. Because more applications of DSmT have emerged in the past years since the apparition of the fourth book of DSmT in 2015, the second part of this volume is about selected applications of DSmT mainly in building change detection, object recognition, quality of data association in tracking, perception in robotics, risk assessment for torrent protection and multi-criteria decision-making, multi-modal image fusion, coarsening techniques, recommender system, levee characterization and assessment, human heading perception, trust assessment, robotics, biometrics, failure detection, GPS systems, inter-criteria analysis, group decision, human activity recognition, storm prediction, data association for autonomous vehicles, identification of maritime vessels, fusion of support vector machines (SVM), Silx-Furtif RUST code library for information fusion including PCR rules, and network for ship classification. Finally, the third part presents interesting contributions related to belief functions in general published or presented along the years since 2015. These contributions are related with decision-making under uncertainty, belief approximations, probability transformations, new distances between belief functions, non-classical multi-criteria decision-making problems with belief functions, generalization of Bayes theorem, image processing, data association, entropy and cross-entropy measures, fuzzy evidence numbers, negator of belief mass, human activity recognition, information fusion for breast cancer therapy, imbalanced data classification, and hybrid techniques mixing deep learning with belief functions as well. (shrink)

With the publication of A Theory of Justice in 1971, John Rawls not only rejuvenated contemporary political philosophy but also defended a Kantian form of Enlightenment liberalism called “justice as fairness.” Enlightenment liberalism stresses the development and exercise of our capacity for autonomy, while Reformation liberalism emphasizes diversity and the toleration that encourages it. These two strands of liberalism are often mutually supporting, but they conflict in a surprising number of cases, whether over the accommodation of group difference, the design (...) of civic education, or the promotion of liberal values internationally. During the 1980’s, however, Rawls began to jettison key Kantian characteristics of his theory, a process culminating in the 1993 release of Political Liberalism and completing the transformation of justice as fairness into a Reformation liberalism. -/- Reconstructing Rawls argues that this transformation was a tragic mistake because it jeopardized the most important features of his theory, viz. the lexical priorities of right, liberty, and fair equality of opportunity as well as the difference principle. Controversially, this book contends that Rawls’s so-called “political turn,” motivated by a newfound interest in diversity and the accommodation of difference, has been unhealthy for autonomy-based liberalism and has pushed liberalism more broadly towards cultural relativism, be it in the guise of liberal multiculturalism or critiques of cosmopolitan distributive-justice theories. The book then demonstrates that the central elements of justice as fairness can only be defended within the context of a Kantian Enlightenment liberalism and that Rawls’s hope for a more pluralistic grounding for his theory, endorsed by a wide variety of belief systems present in modern democratic societies, is illusory. -/- Reconstructing Rawls is the first book to systematically compare Rawls’s and Kant’s theories and the first to offer an internal critique and reconstruction of justice as fairness, reconceiving it as a comprehensive, universalistic Kantian liberalism. By doing so, it gives us both the vision of a liberal world order—“a republicanism of all states, together and separately,” as Kant put it—and a mode of justification addressed to all men and women, not as members of particular nations, races, and faiths, but as human beings, as citizens of the world. In short, it reclaims Rawls for the Enlightenment. (shrink)

Culture or Biology? The question can seem deep and important. Yet, I argue in this chapter, if you are enthralled by questions about our biological differences, then you are probably confused. My goal is to diagnose the confusion. In debates about the role of biology in the social world it is easy to ask the wrong questions, and it is easy to misinterpret the scientific research. We are intuitively attracted to what is called psychological essentialism, and therefore interpret what is (...) biological as what can be traced to “essences”. On this interpretation, it would be deep and important to know what about, say, the differences between the genders is biological: it would correspond to what is essential to being a man or being a woman, and be opposed to what is a mere accidental feature that some women or some men have. Yet, the psychological essentialist understanding of ‘biological differences’ is deeply mistaken about biology. It has the wrong conception of biological kinds, of biological heritability, and of how genes and hormones work. Those who argue for an important role of ‘biology’ in the explanation of human differences often see ‘the science’ on their side. But this is false – on the interpretation of ‘biological differences’ that is most intuitive and that makes the question appear to be most interesting. Defenders of ‘biology’ often have the science against them. What is often called ‘biology’ is a myth: a myth created by an intuitive tendency that grotesquely distorts real biological research. (shrink)

Culture as a dynamic system of meaningful relations can naturally accommodate a hermeneutic analysis. In this essay, the notion of Gadamer’s hermeneutics as involving interpretable meaning throughout experiential reality permits a natural concordance with an understanding of culture as meaningful. The Gadamerian idea that prejudices inform the horizons that make our experiences intelligible is applied to the view that culture is both a self-enclosed structure that is given by one’s horizon and one that continuously points past this horizon in genuine (...) dialogue. Nevertheless, in seeing culture as a coherent system that transcends itself, we are consequently faced with a dilemma regarding the evolution of one’s cultural horizons: whether past horizons can survive the creation of novel ones through dialogue. However, this may be resolved through Gadamer’s understanding of the functions of sameness and difference within horizonal evolution, and how these functions feature in the distinction between a shared ontological ground and the horizons through which the ground is interpreted. Ultimately, we showcase how it is noncontradictory to suppose that culture is both self- and other-referential. (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)

Smash the System! Punk Anarchism as a Culture of Resistance offers a snapshot of anarchist punk as a culture of resistance across the globe. In these diverse and internationalist chapters we witness struggles against racism and colonialism in South Africa, resistance to neo-liberalism and state oppression in Latin America, resistance to police brutality and capitalism in Western, Central and Southeast Europe, struggles for equality and against patriarchy in the US, and anarchist resistance against injustice and authoritarianism in Asia. The common (...) theme is that anarchist punks have consistently sought to SMASH THE SYSTEM, whether that system is capitalism, state socialism, authoritarian communism, the police state, patriarchy, racism, ethno-nationalism, fascism, homophobia, colonialism, neo-liberalism, or the military industrial complex. In doing so anarchist punks have built thriving and diverse cultures of resistance and revitalised the anarchist movement across the world. -/- . (shrink)