Menary OpenMIND, MIND Group, Frankfurt am Main, 2015) has argued that the development of our capacities for mathematical cognition can be explained in terms of enculturation. Our ancient systems for perceptually estimating numerical quantities are augmented and transformed by interacting with a culturally-enriched environment that provides scaffolds for the acquisition of cognitive practices, leading to the development of a discrete number system for representing number precisely. Numerals and the practices associated with numeral systems play a significant role (...) in this process. However, the details of the relationship between the ancient number system and the discrete number system remain unclear. This lack of clarity is exacerbated by the problem of symbolic estrangement and the fact that unique features of how numeral systems represent require our ancient number system to play a dual role. These issues highlight that Dehaene’s From monkey brain to human brain, MIT Press, Cambridge, pp 133–157, 2005) neuronal recycling hypothesis may be insufficient to explain the neural mechanisms underlying the process of enculturation. In order to explain mathematical enculturation, and enculturation more generally, it may be necessary to adopt Anderson’s :245–266, 2010; After phrenology: neural reuse and the interactive brain, MIT Press, Cambridge, 2014) theory of neural reuse. (shrink)

In recent decades, non-representational approaches to mental phenomena and cognition have been gaining traction in cognitive science and philosophy of mind. In these alternative approach, mental representations either lose their central status or, in its most radical form, are banned completely. While there is growing agreement that non-representational accounts may succeed in explaining some cognitive capacities, there is widespread skepticism about the possibility of giving non-representational accounts of cognitive capacities such as memory, imagination or abstract thought. In this paper, I (...) will critically examine the view that there are fundamental limitations to non-representational explanations of cognition. Rather than challenging these arguments on general grounds, I will examine a set of human cognitive capacities that are generally thought to fall outside the scope of non-representational accounts, i.e. numerical cognition. After criticizing standard representational accounts of numerical cognition for their lack of explanatory power, I will argue that a non-representational approach that is inspired by radical enactivism offers the best hope for developing a genuine naturalistic explanatory account for these cognitive capacities. (shrink)

There is a category of objects such that for any two occurrences of an object in that category, Establishing the highest degree of their qualitative identity will not be sufficient to establish that the object involved is one and the same. It is first argued that objects in this category occupy positions in a spatio-Temporal continuum and obey certain principles of conservation. And then two criteria for the numerical identity of these objects are developed: (a) that there are scientific (...) laws which can, In principle, Predict or retrodict a continuous path for the object; (b) that the parts of the object and their arrangement are preserved in a certain specified way. (shrink)

The study of neuronal specialisation in different cognitive and perceptual domains is important for our understanding of the human brain, its typical and atypical development, and the evolutionary precursors of cognition. Central to this understanding is the issue of numerical representation, and the question of whether numbers are represented in an abstract fashion. Here we discuss and challenge the claim that numerical representation is abstract. We discuss the principles of cortical organisation with special reference to number and (...) also discuss methodological and theoretical limitations that apply to numerical cognition and also to the field of cognitive neuroscience in general. We argue that numerical representation is primarily non-abstract and is supported by different neuronal populations residing in the parietal cortex. (shrink)

Arithmetic is one of the foundations of our educational systems, but what exactly is it? Numbers are everywhere in our modern societies, but what is our knowledge of numbers really about? This book provides a philosophical account of arithmetical knowledge that is based on the state-of-the-art empirical studies of numerical cognition. It explains how humans have developed arithmetic from humble origins to its modern status as an almost universally possessed knowledge and skill. Central to the account is the realisation (...) that, while arithmetic is a human creation, the development of arithmetic is constrained by our evolutionarily developed cognitive architecture. Arithmetic is a sophisticated cultural development, but it is ultimately based on abilities with numerosities that we already possess as infants and share with many non-human animals. Therefore, arithmetic is not purely conventional, an arbitrary game akin to chess. Instead, arithmetic is deeply connected to our basic cognitive capacities. (shrink)

In philosophical studies regarding mathematical models of dynamical systems, instability due to sensitive dependence on initial conditions, on the one side, and instability due to sensitive dependence on model structure, on the other, have by now been extensively discussed. Yet there is a third kind of instability, which by contrast has thus far been rather overlooked, that is also a challenge for model predictions about dynamical systems. This is the numerical instability due to the employment of numerical methods (...) involving a discretization process, where discretization is required to solve the differential equations of dynamical systems on a computer. We argue that the criteria for numerical stability, as usually provided by numerical analysis textbooks, are insufficient, and, after mentioning the promising development of backward analysis, we discuss to what extent, in practice, numerical instability can be controlled or avoided. (shrink)

This article addresses the physical chemical processes underlying biological self-organisation by which a homogenous solution of reacting chemicals spontaneously self-organises. Theoreticians have predicted that self-organisation can arise from a coupling of reactive processes with molecular diffusion. In addition, the presence of an external field, such as gravity, at a critical moment early in the process may determine the morphology that subsequently develops. The formation, in-vitro, of microtubules, a constituent of the cellular skeleton, shows this type of behaviour. The preparations spontaneously (...) self-organise by reaction-diffusion and the morphology that develops depends upon the presence of gravity at a critical bifurcation time early in the process. Here, we present numerical simulations of a population of microtubules that reproduce this behaviour. Microtubules can grow from one end whilst shrinking from the other. The shrinking end leaves behind a chemical trail of high tubulin concentration. Neighbouring microtubules preferentially grow into these regions, whilst avoiding regions of low tubulin concentration. The chemical trails produced by individual microtubules thus activate and inhibit the formation of neighbouring microtubules and this progressively leads to self-organisation. Gravity acts by way of its directional interaction with the macroscopic density fluctuations present in the solution arising from microtubule disassembly. (shrink)

In a recent paper, Chunghyoung Lee argues that, because zygotes are developmentally plastic, they cannot be numerically identical to the singletons into which they develop, thereby undermining conceptionism. In this short paper, I respond to Lee. I argue, first, that, on the most popular theories of personal identity, zygotic plasticity does not undermine conceptionism, and, second, that, even overlooking this first issue, Lee’s plasticity argument is problematic. My goal in all of this is not to take a stand in the (...) abortion debate, which I remain silent on here, but, rather, to push for the conclusion that transitivity fails when we are talking about numerical identity of non-abstract objects. (shrink)

Numerous philosophers in recent decades have argued that a partial explanation for how the blessed in heaven are impeccable while remaining free and responsible is that they have cultivated or developed such a virtuous character prior to heaven that once in heaven they are incapable of acting contrary to their virtuously cultivated characters. Further, because the agents are at least partially responsible for the construction of their characters, they can be considered free and responsible with regard to the choices or (...) actions such virtuous characters allow. In what follows I will argue that the impeccability of the blessed is not achieved through a character-development process performed by the blessed themselves. (shrink)

Past and present societies world-wide have employed well over 100 distinct notational systems for representing natural numbers, some of which continue to play a crucial role in intellectual and cultural development today. The diversity of these notations has prompted the need for classificatory schemes, or typologies, to provide a systematic starting point for their discussion and appraisal. The present paper provides a general framework for assessing the efficacy of these typologies relative to certain desiderata, and it uses this framework (...) to discuss the two influential typologies of Zhang & Norman and Chrisomalis. Following this, a new typology is presented that takes as its starting point the principles by which numerical notations represent multipliers (the principles of cumulation and cipherization), and bases (those of integration, parsing, and positionality). Many different examples show that this new typology provides a more refined classification of numerical notations than the ones put forward previously. In addition, the framework provided here can be used to assess typologies not only of numerical notations, but also of many other domains. (shrink)

This book presents a philosophical interpretation to numerical cognition based on dual process theories and heuristics. It shows how investigations in cognitive science can shed light on issues traditionally raised by philosophers of mathematics. The analysis will also help readers to better understand the relationship between current neuroscientific research and the philosophical reflection on mathematics. The author seeks to explain the acquisition of mathematical concepts. To accomplish this, he needs to answer two questions. How can the concepts of approximate (...) numerosity become an object of thought that is so accessible to our consciousness? How are these concepts refined and specified in such a way as to become numbers? Unfortunately, there is currently no model that can truly demonstrate the role of language in the development of numerical skills starting from approximate pre-verbal skills. However, the author details a solution to this problem: dual process theories. It is an approach widely used by theorists focusing on reasoning, decision making, social cognition, and consciousness. Here, he applies this approach to the studies on mathematical knowledge. He details the results brought about by psychological and neuroscientific studies conducted on numerical cognition by key neuroscientists. In the process, he develops the foundations of a new, potential philosophical explanation on mathematical knowledge. (shrink)

ArgumentJohannes Kepler published hisAstronomia novain 1609, based upon a huge amount of computations. The aim of this paper is to show that Kepler's new astronomy was grounded on methods from numerical analysis. In his research he applied and improved methods that required iterative calculations, and he developed precompiled mathematical tables to solve the problems, including a transcendental equation. Kepler was aware of the shortcomings of his novel methods, and called for a new Apollonius to offer a formal mathematical deduction. (...) He was also in great need of computational power, and his friend and colleague, Wilhelm Schickard, constructed the first prototype of a true mechanical calculator, although it never came into regular use. The article concludes that Kepler's new astronomy was clearly backed up by numerical methods and embedded concepts and challenges of great importance for the future development of numerical analysis. (shrink)

In this paper I study the development of arithmetical cognition with the focus on metaphorical thinking. In an approach developing on Lakoff and Núñez, I propose one particular conceptual metaphor, the Process → Object Metaphor, as a key element in understanding the development of mathematical thinking.

An interpretive system for the IBM 704 computer permitting interpretation of the genetic pattern of a numeric symbioorganism as a game strategy has been developed. Selection for best performance in a simple game has been applied in a preliminary experiment. An objective method to measure the quality of a game played is described. The results presented in the article show a small but significant improvement of game quality during a period of 2300 generations.The general characteristics of the phenomena observed are (...) similar to those of preceding evolution experiments . However, a startling infection process caused by a parasite whose behaviour was influenced by the game competition is described. The parasite never developed an independent game strategy to any degree of efficiency and was entirely dependent on its host organism for game competitions with, and transmission of the infection to, uninfected hosts.The consequences of substituting the reproduction and mutation rules used in the preceding evolution experiments are discussed. Particularly, the use of rules applying the reproduction pattern ofDNA-molecules is considered, and the theoretic aspects of symbiogenetic evolution experiments based onDNA-norm are discussed. A few inferences concerning the origin and history of terrestrial life suggested by the results of the symbiogenesis experiments are presented.Ein interpretierendes System für die IBM 704 Rechenmaschine, dass Interpretation des genetischen Modells von einem numerischen Symbio-organismus wie eine Spiel Strategie, erlaubt, wurde entwickelt. Eine Forführung für Fähigkeit in einem einfachen Spiel wurde angewandt in einem preliminarisches Experiment. Eine objektive Methode zur Messung der Qualität des betreffenden Spiels wurde beschrieben. Die in dem Artikel angegebenen Resultate zeigen eine kleine, aber bedeutende Verbesserung der Spiel-Qualität während einr Periode von 2300 Generationen.Die allgemeinen Kennziechen von den beobachteten Phänomenen sind denen von vorhergehenden Evolutions-Experimenten ähnlich . Jedoch, ein überraschender Infektions-Prozess, verursacht durch einen Parasit, wessen Verhalten beinflusst wurde durch die Spiel-Konkurrenz, wurde beschrieben. Der Parasit entwickelte niemals eine unabhängige Spiel-Strategie zu irgendeinem Masze von Fähigkeit und war ganz abhängig von seinem Gastherr-Organismus für Spiel-Konkurrenz mit, und Überbringung von der Infektion auf, uninfektierte Gäste.Die Folgerungen von dem Ersetzen der Fortpflanzung und Mutations-Regeln , angewandt in vorhergehenden Evolutions-Experimente wurden besprochen. Besonders der Gebrauch von Regeln welche das FortpflanzungsModell von DNA-Molekülen anwenden wurde betrachtet, und die theorethischen Aspekte von Symbiogenetischen Evolutions-Experimenten basiert auf DNA-Norm wurden besprochen. Einige Schlussfolgerungen in Bezug auf die Entstehung und Geschichte von dem Erdenleben suggeriert durch die Resultate von den Symbiogenese-Experimenten wurden gezeigt. (shrink)

Energy contributes significantly in almost all aspects of human life as well as economic activities and plays a crucial role in the infrastructural development of a county to alleviate poverty. Generating energy from a renewable source such as small hydropower through the application of pump operating as a turbine mode called Pump as Turbine is one of the best alternatives to provide clean and inexpensive energy. Using Pump as Turbine helps in generating reasonably priced hydroelectric power for communities in (...) underdeveloped counties. This study investigates the effects of internal flow behaviour and performance of Pump as Turbine under different rotational speed and flow rate. The rotational speed is an essential physical parameter as it affects the Pump as Turbine operation. A model-specific speed centrifugal pump model with head 32, flow rate of 12.5 and the rotational speed of 2900 rpm, has been selected for the study. Numerical simulations have been conducted using the k-ω turbulence model to solve three-dimensional equations. The pump mode experimental data were used to confirm the results for better analysis. The results predicted that vortex and turbulent kinetic energy increase per rotational speed increase. Also, at the higher rotational speed, very high recirculation of flow is detected at the blade suction chamber, although the pressure side has a smooth flow. This study provides beneficial information which will serve as a reference to help improve PAT performance along with selecting PAT for a small hydropower site. Future works will consider the impact of blade thickness and cavitation in Pump as Turbine. (shrink)

In this chapter we consider the theories of embodied cognition and extended mind with respect to the human ability to engage in numerical cognition. Such an enquiry requires first distinguishing between our innate number sense and the sort of numerical reasoning that is unique to humans. We provide anthropological and linguistic research to defend the thesis that places the body at the center of our development of numerical reasoning. We then draw on archaeological research to suggest (...) a rough date for when ancient humans first were able to represent numerical information beyond the body and in enduring material artifacts. We conclude by briefly describing how these capacities for embodied and extended numerical cognition shaped our world. (shrink)

Our epistemic access to mathematical objects, like numbers, is mediated through our external representations of them, like numerals. Nevertheless, the role of formal notations and, in particular, of the internal structure of these notations has not received much attention in philosophy of mathematics and cognitive science. While systems of number words and of numerals are often treated alike, I argue that they have crucial structural differences, and that one has to understand how the external representation works in order to form (...) an advanced conception of numbers. The relation between external representations and mathematical cognition will be discussed by drawing on experimental results from cognitive science and mathematics education, and I argue for the constitutive role of external representations for the development of an advanced conception of numbers. (shrink)

The domain of numbers provides a paradigmatic case for investigating interactions of culture, language, and cognition: Numerical competencies are considered a core domain of knowledge, and yet the development of specifically human abilities presupposes cultural and linguistic input by way of counting sequences. These sequences constitute systems with distinct structural properties, the cross-linguistic variability of which has implications for number representation and processing. Such representational effects are scrutinized for two types of verbal numeration systems—general and object-specific ones—that were (...) in parallel use in several Oceanic languages. The analysis indicates that the object-specific systems outperform the general systems with respect to counting and mental arithmetic, largely due to their regular and more compact representation. What these findings reveal on cognitive diversity, how the conjectures involved speak to more general issues in cognitive science, and how the approach taken here might help to bridge the gap between anthropology and other cognitive sciences is discussed in the conclusion. (shrink)

This article presents research on assemblages among humans and computational systems in which physical and virtual autonomous processes occur in order to create artworks allowing the emergence of mixed sensory set-ups. It begins with triadic relationships computer, physical objects and participants aimed at co-relations among bands of bots (virtual and physical) with groups of humans (interactors). The bots have a representation of the virtual world: physical bots live on a flat surface (Abbot 1991), a projection of the 3D environment where (...) the virtual bots live. The artwork also explores the metaphor of higher dimensions being understood through their projections in lower dimensions. Its goal is to weave interaction and autonomous processes, looking for poetic results integrating art, science and technology; results with aesthetic, poetic and functional qualities; and results exploring emergency and agency for design, construction and set-up of expressive systems. For these symbioses to happen the assemblage of environments with aesthetic and poetic appeal leads one to think about mixed cognitive processes that provoke emergent behaviours. I am interested in the behaviours emerged in such inter-relationships. Therefore, to achieve this goal, I have created a Java framework that allows me to program interfaces weaving such behaviors1 and also I have programmed a set of sketches using Processing2 to test the hypothesis. The main inquiries of such research are as follows: What kind of artwork could mix people with autonomous computational processes without becoming invasive? and Is such a dichotomy possible? To answer these questions, I came up with the idea of playing with swarms and flock algorithms mixing virtual and physical domains. Will this create the mixed behaviour I am looking for? Will the participants contribute with their actions, emotions and affects while the computer develops its own autonomous processes? (shrink)

We concur with Cohen Kadosh & Walsh (CK&W) that representation of numbers in the parietal cortex is format dependent. In addition, we suggest that all formats do not automatically, and equally, access analog magnitude representation in the intraparietal sulcus (IPS). Understanding how development, learning, and context lead to differential access of analog magnitude representation is a key question for future research.

Due to their frequent uneven cognitive profiles, genetic developmental disorders allow researchers to investigate which numerical sub-system of those present in typically developing infants best predicts subsequent numerical abilities. More importantly, they can provide evidence of which other cognitive abilities outside number are necessary for the successful development of these numerical sub-systems. We discuss evidence from cross-syndrome comparisons of adults, adolescents, children, and infants with Williams syndrome and those with Down syndrome to show that the approximate (...) magnitude sub-system is crucial for later number development. In addition, we show that specific problems outside the number domain, and within basic-level visual and attention systems contribute to an explanation of the difficulties and proficiencies observed within each genetic disorder. Finally, we argue that a truly developmental approach is critical when using the cross-syndrome design in order to reveal subtle differences that impact over time on the development of cognitive abilities. (shrink)

Solid-state processing of metal material is a very complex physical and chemical process, which is coupled by a series of variations including heat transfer, momentum transfer, mass transfer, and phase change. Applying three-dimensional finite element numerical method to the simulation of solid-state processing can perform analysis of metal material’s forging processes before production trial production, can obtain their relevant information such as material flow law, temperature field, and strain field under the minimum physical test conditions, thereby predicting metal material’s (...) forming defects and improving their forging quality. On the basis of summarizing and analyzing previous research works, this paper expounded the current status and significance of solid-state processing of metal materials, elaborated the development background, current status, and future challenges of 3D finite element numerical simulation, introduced the discrimination method and free surface solution method of numerical simulation calculation, conducted finite element model’s geometric assumptions, material selection, element division, model establishment, parameter selection, and initial and boundary condition determination, and simulated and analyzed rheological casting, remelting heating, thixoforming, and rotary piercing processes of metal materials. The results show that the 3D finite element numerical method can not only simulate various processes of flow field, temperature field, stress field, and microstructure in solid-state processing but also can provide a reliable basis for effectively obtaining a reasonable description and finding a more optimized design plan for metal material processing in a short time, which plays an important role in understanding and analyzing solid metal forming process, controlling and optimizing process parameters, guiding and mastering rheological casting, and secondary heating and rotary piercing of metal materials. (shrink)

In his essay Thinking Colours and/or Machines Kittler hints at a key point in the emergence of modern European culture: the point at which ‘letters and numbers no longer coincide’. In this essay - first published in 2003 as Zahl und Ziffer - Kittler traces the split between numerals and numbers in sweeping historical detail. This is part of a much larger project, the aim of which is to think about technology, history and culture anew by considering the ways in (...) which ‘letters, numbers, images and tones’ have been differentiated and re-integrated by developing notation systems and media technologies. In this present essay, Kittler is concerned specifically with the question of number. His argument is that numbers and numerals have not always stood apart. In Old Hebrew and even nursery rhymes, for example, numbers are in fact words. This might seem like a banal observation, but for Kittler it is crucial as historically, mathematics proper only developed ‘in cultures in which numbers are present as numerals’, a development which entailed the transformation of numbers from signifiers into signifieds and which rested on the emergence of storage and transmission media that Kittler calls ‘the media of mathematics’. This connection between media and mathematics is explored through a wide range of philosophical sources: Plato, Philolaus, Aristotle and Aquinas, to name but a few. Kittler is fascinated by the inscription technologies that make mathematics possible, and which at the same time structure cultural forms as well as our bodily experience of them. As he puts it in a programmatic aside, ‘media studies only make sense’ if they focus on how ‘media make senses.’ Hence his focus on the Greek phonetic alphabet: for Kittler, its superiority has less to do with its ability to reproduce the spoken words of any language, than with the fact that at one point it was used to handle language, music, and mathematics - that is, one and the same set of signs was used to encode letters, tones and numbers. This, however, was not an abstract undertaking but developed in constant feedback with specific instruments or media, especially the lyre and the bow. It was here that fundamental concepts such as logoi were first developed that were subsequently distorted, misunderstood and deprived of their musico-technical origins by philosophers such as Aristotle. Kittler’s essay is thus also part of a larger cultural project, indebted in particular to Martin Heidegger, whose aim it is to ferret out the different, as yet unrevealed beginning of occidental culture. Moreover, while it was necessary for the evolution of modern mathematics that numbers receive a notation system of their own that will allow for ratios and decimals, among others, it is obvious that Kittler sees the computer as a return of universal alphabet that operates in constant feedback with a medium that shapes our senses: ‘In the Greek alphabet our senses were present - and thanks to Turing they are so once again.’. (shrink)

In Concepts, Kinds, and Cognitive Development, Frank C. Keil provides a coherent account of how concepts and word meanings develop in children, adding to our understanding of the representational nature of concepts and word meanings at all ages. Keil argues that it is impossible to adequately understand the nature of conceptual representation without also considering the issue of learning. Weaving together issues in cognitive development, philosophy, and cognitive psychology, he reconciles numerous theories, backed by empirical evidence from nominal (...) kinds studies, natural-kinds studies, and studies of fundamental categorical distinctions. He shows that all this evidence, when put together, leads to a better understanding of semantic and conceptual development. The book opens with an analysis of the problems of modeling qualitative changes in conceptual development, investigating how concepts of natural kinds, nominal kinds, and artifacts evolve. The studies on nominal kinds document a powerful and unambiguous developmental pattern indicating a shift from a reliance on global tabulations of characteristic features to what appears to be a small set of defining ones. The studies on natural kinds document an analogous shift toward a core theory instead of simple definition. Both sets of studies are strongly supported by cross cultural data. While these patterns seem to suggest that the young child organizes concepts according to characteristic features, Keil argues that there is a framework of conceptual categories and causal beliefs that enables even very young children to understand kinds at a deeper, theoretically guided, level. This account suggests a new way of understanding qualitative change and carries strong implications for how concepts are represented at any point in development. A Bradford Book. (shrink)

This paper is based on ethnographic research of data practices in a public health project called Weather Health and Air Pollution. I examine two different kinds of practices that make air pollution data, focusing on how they relate to particular modes of sensing and articulating air pollution. I begin by describing the interstitial spaces involved in making measurements of air pollution at monitoring sites and in the running of a computer simulation. Specifically, I attend to a shared dimension of these (...) practices, the checking of a numerical reading for error. Checking a measurement for error is routine practice and a fundamental component of making data, yet these are also moments of interpretation, where the form and meaning of numbers are ambiguous. Through two case studies of modelling and monitoring data practices, I show that making a ‘good’ measurement requires developing a feeling for the instrument–air pollution interaction in terms of the intended functionality of the measurements made. These affective dimensions of practice are useful analytically, making explicit the interaction of standardised ways of knowing and embodied skill in stabilising data. I suggest that environmental data practices can be studied through researchers’ materialisation of error, which complicate normative accounts of Big Data and highlight the non-linear and entangled relations that are at work in the making of stable, accurate data. (shrink)

This article seeks to provide a comprehensive re-evaluation of the redistributive models of democracy advanced by Carles Boix, and Daron Acemoglu and James Robinson, their reception within the democratization literature, and the subsequent trajectories of their authors. Contrary to the existing literature, which commonly envisions RMDs as a unified framework, this article argues that Boix and Acemoglu and Robinson’s models should be understood as divergent theories of democratic transitions. In the aftermath of numerous criticisms, both authors have developed sharply different (...) understandings of democratization. We argue that Acemoglu and Robinson have backtracked from their original formulation toward a “Whiggish” history of the rise of liberty, while Boix has increasingly reverted to the core propositions of classical modernization theory. In the process, this article argues that RMDs have lost, and reneged on, much of their apparent explanatory power regarding transitions to and reversions from democracy. (shrink)

Leibovich et al. challenge the prevailing view that non-symbolic number sense is innate, that detection of numerosity is distinct from detection of continuous magnitude. In the present commentary, the authors' viewpoint is discussed in light of the integrative theory of numerical development along with implications for understanding mathematics disabilities.

It has been generally assumed that certain categories of numerical expressions, such as ‘more than n’, ‘at least n’, and ‘fewer than n’, systematically fail to give rise to scalar implicatures in unembedded declarative contexts. Various proposals have been developed to explain this perceived absence. In this paper, we consider the relevance of scale granularity to scalar implicature, and make two novel predictions: first, that scalar implicatures are in fact available from these numerical expressions at the appropriate granularity (...) level, and second, that these implicatures are attenuated if the numeral has been previously mentioned or is otherwise salient in the context. We present novel experimental data in support of both of these predictions, and discuss the implications of this for recent accounts of numerical quantifier usage. (shrink)

The correlation coefficient between two variables plays an important role in statistics. Also, the accuracy of relevance assessment depends on information from a set of discourses. The data collected from numerous statistical studies are full of exceptions. The Pythagorean fuzzy hypersoft set is a parameterized family that deals with the subattributes of the parameters and an appropriate extension of the Pythagorean fuzzy soft set. It is also the generalization of the intuitionistic fuzzy hypersoft set, which is used to accurately assess (...) insufficiency, anxiety, and uncertainties in decision-making. The PFHSS can accommodate more uncertainties compared to the IFHSS, and it is the most substantial methodology to describe fuzzy information in the decision-making process. The core objective of the this study is to develop the notion and features of the correlation coefficient and the weighted correlation coefficient for PFHSS and to introduce the aggregation operators such as Pythagorean fuzzy hypersoft weighted average and Pythagorean fuzzy hypersoft weighted geometric operators under the PFHSS scenario. A prioritization technique for order preference by similarity to the ideal solution under PFHSS based on correlation coefficients and weighted correlation coefficients is presented. Through the developed methodology, a technique for solving multiattribute group decision-making problem is planned. Also, the importance of the developed methodology and its application in indicating multipurpose antivirus mask throughout the COVID-19 pandemic period is presented. A brief comparative analysis is described with the advantages, effectiveness, and flexibility of numerous existing studies that demonstrate the effectiveness of the proposed method. (shrink)

This book is open access under a CC BY-NC 2.5 license. This book offers a devastating look at deeply flawed development processes driven by international finance, African governments and the global consulting industry. It examines major river basin development underway in the semi-arid borderlands of Ethiopia, Kenya and South Sudan and its disastrous human rights consequences for a half-million indigenous people. The volume traces the historical origins of Gibe III megadam construction along the Omo River in Ethiopia-in turn, (...) enabling irrigation for commercial-scale agricultural development and causing radical reduction of downstream Omo and (Kenya's) Lake Turkana waters. Presenting case studies of indigenous Dasanech and northernmost Turkana livelihood systems and Gibe III linked impacts on them, the author predicts agropastoral and fishing economic collapse, region-wide hunger with exposure to disease epidemics, irreversible natural resource destruction and cross-border interethnic armed conflict spilling into South Sudan. The book identifies fundamental failings of government and development bank impact assessments, including their distortion or omission of mandated transboundary assessment, cumulative effects of the Gibe III dam and its linked Ethiopia-Kenya energy transmission 'highway' project, key hydrologic and human ecological characteristics, major earthquake threat in the dam region and widespread expropriation and political repression. Violations of internationally recognized human rights, especially by the Ethiopian government but also the Kenyan government, are extensive and on the increase-with collaboration by the development banks, in breach of their own internal operational procedures. A policy crossroads has now emerged. The author presents the alternative to the present looming catastrophe-consideration of development suspension in order to undertake genuinely independent transboundary assessment and a plan for continued development action within a human rights framework-forging a sustainable future for the indigenous peoples now directly threatened and for their respective eastern Africa states. Claudia Carr's book is a treasure of detailed information gathered over many years concerning river basin development of the Omo River in Ethiopia and its impact on the peoples of the lower Omo Basin and the Lake Turkana region in Kenya. It contains numerous maps, charts, and photographs not previously available to the public. The book is highly critical of the environmental and human rights implications of the Omo River hydropower projects on both the local ethnic communities in Ethiopia and on the downstream Turkana in Kenya. David Shinn Former Ambassador to Ethiopia and to Burkina Faso Adjust Professor of International Affairs, The George Washington University, Washington D.C. (shrink)

Numerous recent discoveries in China of ancient tombs have greatly increased our knowledge of ritual and religious practices. These discoveries include excavated oracle bones, bronze, jade, stone and pottery objects, and bamboo manuscripts dating from the twelfth to fourth century BCE. Inscribed upon these artifacts are a large number of records of numerical sequences, for which no explanation has been found of how they were produced. Structural links to the Book of Changes, a divination manual that entered the Confucian (...) canon, are evident; yet, the algorithm described therein dates to the slightly later second to first century BCE. By combining archeological and statistical evidence, we propose a new methodology that enables us to reconstruct and test cleromantic techniques which can explain how these numerical sequences were generated. Dice and divination stalk use, either in combination or separately, appear in fact to have been underlying the rather stable numerical patterns in ancient China all the way back to the late Shang dynasty (1300–1046 BCE). Bringing to light such a long-standing technique, which awaits further confirmation from the ever-growing database of newly discovered numerical and textual records, can change drastically our understanding of early Chinese history and of the historical development of sophisticated arithmetical practices and the rationalization of chance. (shrink)

Why would we want to develop artificial human-like arithmetical intelligence, when computers already outperform humans in arithmetical calculations? Aside from arithmetic consisting of much more than mere calculations, one suggested reason is that AI research can help us explain the development of human arithmetical cognition. Here I argue that this question needs to be studied already in the context of basic, non-symbolic, numerical cognition. Analyzing recent machine learning research on artificial neural networks, I show how AI studies could (...) potentially shed light on the development of human numerical abilities, from the proto-arithmetical abilities of subitizing and estimating to counting procedures. Although the current results are far from conclusive and much more work is needed, I argue that AI research should be included in the interdisciplinary toolbox when we try to explain the development and character of numerical cognition and arithmetical intelligence. This makes it relevant also for the epistemology of mathematics. (shrink)

Quantifiers are a test case for an interface between psychological questions, which attempt to specify the numerical content that supports the semantics of quantifiers, and linguistic questions, which uncover the range of possible quantifier meanings allowable within the constraints of the syntax. Here we explore the development of comprehension of most in English, of particular interest as it calls on precise numerical content that, in adults, requires an understanding of large exact numerosities (e.g., 23 blue dots and (...) 17 yellow is an instance of “most of the dots are blue”). In a sample of 100 children 2 to 5 years of age we find that (a) successful most comprehension in cases with two salient subsets is achieved at 3 years, 7 months of age, and (b) most comprehension is independent of knowledge of large exact number words; that is, knowledge of large exact number words is neither necessary, as evidenced by children who understand “most” but not “four,” nor sufficient, as evidenced by children who understand “nine” but not “most.”. (shrink)

Developing earlier studies of the system of numbers in Mundurucu, this paper argues that the Mundurucu numeral system is far more complex than usually assumed. The Mundurucu numeral system provides indirect but insightful arguments for a modular approach to numbers and numerals. It is argued that distinct components must be distinguished, such as a system of representation of numbers in the format of internal magnitudes, a system of representation for individuals and sets, and one-to-one correspondences between the numerosity expressed by (...) the number and its metrics. It is shown that while many-number systems involve a compositionality of units, sets and sets composed of units, few-number languages, such as Mundurucu, do not have access to sets composed of units in the usual way. The nonconfigurational character of the Mundurucu language, which is related to a property for which we coin the term 'low compositionality power', accounts for this and explains the curious fact that Mundurucus make use of marked one-to-one correspondence strategies in order to overcome the limitations of the core system at the perceptual/motor interface of the language faculty. We develop an analysis of a particular construction, parallel numbers, which has not been studied before, elucidating the whole system. This analysis, we argue, sheds new light on classical philosophical, psychological and linguistic debates about numbers and numerals and their relation to language, and more particularly, sheds light on few-number languages. (shrink)

Socio-economic status and mathematical performance seem to be risk factors of mathematics anxiety in both children and adults. However, there is little evidence about how exactly these three constructs are related, especially during early stages of mathematical learning. In the present study, we assessed longitudinal performance in symbolic and non-symbolic basic numerical skills in pre-school and second grade students, as well as MA in second grade students. Participants were 451 children from 12 schools in Chile, which differed in school (...) vulnerability index, an indicator of SES. We tested an explanatory model of MA that included SES and longitudinal performance in basic numerical skills as predictors. The results showed a direct effect of SES on MA and a mediating effect of performance in symbolic and non-symbolic comparison tasks in pre-school. However, in second grade, only performance in symbolic comparison significantly mediated the SES-MA relationship. These findings suggest that performance in non-symbolic comparison plays an important role in explaining MA at initial stages, but that its influence is no longer significant by the time children reach formal instruction in second grade. By contrast, as children’s formal educational experience in mathematics increases, MA becomes linked primarily to symbolic numerical tasks. In sum, SES affects MA and this is due in part to the effect of SES on the development of numerical learning in pre-school, which in turn has an impact on subsequent, more complex learning, ultimately leading to differences in MA. We discuss the implications of these findings for preventing and acting upon the emergence of MA. (shrink)

Since the 1990s, the essential function of teacher trainers in academic courses has gradually attained more attention from scholars. Also, the teacher trainers’ professional development has acquired worldwide attraction following the concept that teacher trainers are deeply liable for educator education quality. The present mini-review of literature indicates that while teacher trainers have several complicated functions, they obtain the least preparation or opportunities for professional development to perform such functions. Consequently, they require getting the related knowledge and skills (...) after accepting the role of teacher trainers. Besides numerous aspects affecting teacher trainers’ professional development, teaching skills, and knowledge have important functions that are at the center of attention in this mini-review of literature. In brief, several implications are presented for the instructional addressees. (shrink)

Previous discussions of the origins of writing in the Ancient Near East have not incorporated the neuroscience of literacy, which suggests that when southern Mesopotamians wrote marks on clay in the late-fourth millennium, they inadvertently reorganized their neural activity, a factor in manipulating the writing system to reflect language, yielding literacy through a combination of neurofunctional change and increased script fidelity to language. Such a development appears to take place only with a sufficient demand for writing and reading, such (...) as that posed by a state-level bureaucracy; the use of a material with suitable characteristics; and the production of marks that are conventionalized, handwritten, simple, and non-numerical. From the perspective of Material Engagement Theory, writing and reading represent the interactivity of bodies, materiality, and brains: movements of hands, arms, and eyes; clay and the implements used to mark it and form characters; and vision, motor planning, object recognition, and language. Literacy is a cognitive change that emerges from and depends upon the nexus of interactivity of the components. (shrink)

The concept of a hypersoft membership function is introduced in the extension of a soft set known as a hypersoft set, permitting it to handle complicated and uncertain information in a more powerful and flexible manner. Many academics have already become fascinated with this new area of study, leading to the development of a number of hybrid structures. This chapter develops some new hybrid hypersoft set structures by taking into account multiple fuzzy set-like settings and possibility degree-based settings collectively. (...) Additionally, numerical examples are included to clarify the concept of these structures. Researchers can utilize this work to better understand and apply a variety of mathematical ideas. (shrink)