Results for 'Number Systems'

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  1. Leibniz on Number Systems.Lloyd Strickland - 2024 - In Bharath Sriraman (ed.), Handbook of the History and Philosophy of Mathematical Practice. Springer. pp. 167-197.
    This chapter examines the pioneering work of Gottfried Wilhelm Leibniz (1646-1716) on various number systems, in particular binary, which he independently invented in the mid-to-late 1670s, and hexadecimal, which he invented in 1679. The chapter begins with the oft-debated question of who may have influenced Leibniz’s invention of binary, though as none of the proposed candidates is plausible I suggest a different hypothesis, that Leibniz initially developed binary notation as a tool to assist his investigations in mathematical problems (...)
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  2. The Small Number System.Eric Margolis - 2020 - Philosophy of Science 87 (1):113-134.
    I argue that the human mind includes an innate domain-specific system for representing precise small numerical quantities. This theory contrasts with object-tracking theories and with domain-general theories that only make use of mental models. I argue that there is a good amount of evidence for innate representations of small numerical quantities and that such a domain-specific system has explanatory advantages when infants’ poor working memory is taken into account. I also show that the mental models approach requires previously unnoticed domain-specific (...)
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  3. Rational Number Representation by the Approximate Number System.Chuyan Qu, Sam Clarke, Francesca Luzzi & Elizabeth Brannon - 2024 - Cognition 250 (105839):1-13.
    The approximate number system (ANS) enables organisms to represent the approximate number of items in an observed collection, quickly and independently of natural language. Recently, it has been proposed that the ANS goes beyond representing natural numbers by extracting and representing rational numbers (Clarke & Beck, 2021a). Prior work demonstrates that adults and children discriminate ratios in an approximate and ratio-dependent manner, consistent with the hallmarks of the ANS. Here, we use a well-known “connectedness illusion” to provide evidence (...)
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  4. Education Enhances the Acuity of the Nonverbal Approximate Number System.Manuela Piazza, Pierre Pica, Véronique Izard, Elizabeth Spelke & Stanislas Dehaene - 2013 - Psychological Science 24 (4):p.
    All humans share a universal, evolutionarily ancient approximate number system (ANS) that estimates and combines the numbers of objects in sets with ratio-limited precision. Interindividual variability in the acuity of the ANS correlates with mathematical achievement, but the causes of this correlation have never been established. We acquired psychophysical measures of ANS acuity in child and adult members of an indigene group in the Amazon, the Mundurucú, who have a very restricted numerical lexicon and highly variable access to mathematics (...)
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  5. Husserl’s Early Genealogy of the Number System.Thomas Byrne - 2019 - Meta: Research in Hermeneutics, Phenomenology, and Practical Philosophy 2 (11):408-428.
    This article accomplishes two goals. First, the paper clarifies Edmund Husserl’s investigation of the historical inception of the number system from his early works, Philosophy of Arithmetic and, “On the Logic of Signs (Semiotic)”. The article explores Husserl’s analysis of five historical developmental stages, which culminated in our ancestor’s ability to employ and enumerate with number signs. Second, the article reveals how Husserl’s conclusions about the history of the number system from his early works opens up a (...)
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  6. The number sense represents (rational) numbers.Sam Clarke & Jacob Beck - 2021 - Behavioral and Brain Sciences 44:1-57.
    On a now orthodox view, humans and many other animals possess a “number sense,” or approximate number system, that represents number. Recently, this orthodox view has been subject to numerous critiques that question whether the ANS genuinely represents number. We distinguish three lines of critique – the arguments from congruency, confounds, and imprecision – and show that none succeed. We then provide positive reasons to think that the ANS genuinely represents numbers, and not just non-numerical confounds (...)
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  7. Numbers, numerosities, and new directions.Jacob Beck & Sam Clarke - 2021 - Behavioral and Brain Sciences 44:1-20.
    In our target article, we argued that the number sense represents natural and rational numbers. Here, we respond to the 26 commentaries we received, highlighting new directions for empirical and theoretical research. We discuss two background assumptions, arguments against the number sense, whether the approximate number system represents numbers or numerosities, and why the ANS represents rational numbers.
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  8. The Dirac large number hypothesis and a system of evolving fundamental constants.Andrew Holster - manuscript
    In his [1937, 1938], Paul Dirac proposed his “Large Number Hypothesis” (LNH), as a speculative law, based upon what we will call the “Large Number Coincidences” (LNC’s), which are essentially “coincidences” in the ratios of about six large dimensionless numbers in physics. Dirac’s LNH postulates that these numerical coincidences reflect a deeper set of law-like relations, pointing to a revolutionary theory of cosmology. This led to substantial work, including the development of Dirac’s later [1969/74] cosmology, and other alternative (...)
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  9. Number Concepts: An Interdisciplinary Inquiry.Richard Samuels & Eric Snyder - 2024 - Cambridge University Press.
    This Element, written for researchers and students in philosophy and the behavioral sciences, reviews and critically assesses extant work on number concepts in developmental psychology and cognitive science. It has four main aims. First, it characterizes the core commitments of mainstream number cognition research, including the commitment to representationalism, the hypothesis that there exist certain number-specific cognitive systems, and the key milestones in the development of number cognition. Second, it provides a taxonomy of influential views (...)
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  10. Does the number sense represent number?Sam Clarke & Jacob Beck - 2020 - In Blair Armstrong, Stephanie Denison, Michael Mack & Yang Xu (eds.), Proceedings of the 42nd Meeting of the Cognitive Science Society.
    On a now orthodox view, humans and many other animals are endowed with a “number sense”, or approximate number system (ANS), that represents number. Recently, this orthodox view has been subject to numerous critiques, with critics maintaining either that numerical content is absent altogether, or else that some primitive analog of number (‘numerosity’) is represented as opposed to number itself. We distinguish three arguments for these claims – the arguments from congruency, confounds, and imprecision – (...)
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  11. Which Parties Count?-The Effective Number of Parties in the Albanian Party System.Anjeza Xhaferaj - 2014 - European Journal of Social Science Education and Research 1 (2):7.
    The aim of this paper is to explore and understand the Albanian Party System. The analysis will cover the period from the collapse of the communist regime in 1991 until 2014. It will try to investigate what forces drive the battle of the parties, what cleavages 'divide' society and consequently the party system as well as which are the parties that count the most. in order to assess this, the paper will focus on the parliamentary parties and will relay on (...)
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  12. A new look at old numbers, and what it reveals about numeration.Karenleigh Anne Overmann - 2021 - Journal of Near Eastern Studies 2 (80):291-321.
    In this study, the archaic counting systems of Mesopotamia as understood through the Neolithic tokens, numerical impressions, and proto-cuneiform notations were compared to the traditional number-words and counting methods of Polynesia as understood through contemporary and historical descriptions of vocabulary and behaviors. The comparison and associated analyses capitalized on the ability to understand well-known characteristics of Uruk-period numbers like object-specific counting, polyvalence, and context-dependence through historical observations of Polynesian counting methods and numerical language, evidence unavailable for ancient numbers. (...)
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  13. Constructing a concept of number.Karenleigh Overmann - 2018 - Journal of Numerical Cognition 2 (4):464–493.
    Numbers are concepts whose content, structure, and organization are influenced by the material forms used to represent and manipulate them. Indeed, as argued here, it is the inclusion of multiple forms (distributed objects, fingers, single- and two-dimensional forms like pebbles and abaci, and written notations) that is the mechanism of numerical elaboration. Further, variety in employed forms explains at least part of the synchronic and diachronic variability that exists between and within cultural number systems. Material forms also impart (...)
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  14. Real Numbers are the Hidden Variables of Classical Mechanics.Nicolas Gisin - 2020 - Quantum Studies: Mathematics and Foundations 7:197–201.
    Do scientific theories limit human knowledge? In other words, are there physical variables hidden by essence forever? We argue for negative answers and illustrate our point on chaotic classical dynamical systems. We emphasize parallels with quantum theory and conclude that the common real numbers are, de facto, the hidden variables of classical physics. Consequently, real numbers should not be considered as ``physically real" and classical mechanics, like quantum physics, is indeterministic.
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  15. Transfinite Number in Wittgenstein's Tractatus.James R. Connelly - 2021 - Journal for the History of Analytical Philosophy 9 (2).
    In his highly perceptive, if underappreciated introduction to Wittgenstein’s Tractatus, Russell identifies a “lacuna” within Wittgenstein’s theory of number, relating specifically to the topic of transfinite number. The goal of this paper is two-fold. The first is to show that Russell’s concerns cannot be dismissed on the grounds that they are external to the Tractarian project, deriving, perhaps, from logicist ambitions harbored by Russell but not shared by Wittgenstein. The extensibility of Wittgenstein’s theory of number to the (...)
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  16. Special Systems Theory.Kent Palmer - manuscript
    A new advanced systems theory concerning the emergent nature of the Social, Consciousness, and Life based on Mathematics and Physical Analogies is presented. This meta-theory concerns the distance between the emergent levels of these phenomena and their ultra-efficacious nature. The theory is based on the distinction between Systems and Meta-systems (organized Openscape environments). We first realize that we can understand the difference between the System and the Meta-system in terms of the relationship between a ‘Whole greater than (...)
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  17. On the basic principle of number.Joosoak Kim - manuscript
    A history of the construction of number has been in line with the process of recognition about the properties of geometry. Natural number representing countability is exhibited on a straight line and the completeness of real number is also originated from the continuous property of the number line. Complex number on a plane off the number line is established and thereafter, the whole number system is completed. When the process of constructing a (...) with geometric features is investigated from different perspectives, it provides a new insight into the fundamental principle of number, which leads to a novel methodology in mathematics. (shrink)
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  18. Theoretical implications of the study of numbers and numerals in mundurucu.Pierre Pica & Alain Lecomte - 2008 - Philosophical Psychology 21 (4):507 – 522.
    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 (...)
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  19. Finger-counting and numerical structure.Karenleigh A. Overmann - 2021 - Frontiers in Psychology 2021 (12):723492.
    Number systems differ cross-culturally in characteristics like how high counting extends and which number is used as a productive base. Some of this variability can be linked to the way the hand is used in counting. The linkage shows that devices like the hand used as external representations of number have the potential to influence numerical structure and organization, as well as aspects of numerical language. These matters suggest that cross-cultural variability may be, at least in (...)
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  20. Husserl’s Early Semiotics and Number Signs: Philosophy of Arithmetic through the Lens of “On the Logic of Signs ”.Thomas Byrne - 2017 - Journal of the British Society for Phenomenology 48 (4):287-303.
    This paper demonstrates that Edmund Husserl’s frequently overlooked 1890 manuscript, “On the Logic of Signs,” when closely investigated, reveals itself to be the hermeneutical touchstone for his seminal 1891 Philosophy of Arithmetic. As the former comprises Husserl’s earliest attempt to account for all of the different kinds of signitive experience, his conclusions there can be directly applied to the latter, which is focused on one particular type of sign; namely, number signs. Husserl’s 1890 descriptions of motivating and replacing signs (...)
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  21. Systems with Single Degree of Freedom and the Interpretation of Quantum Mechanics.Mehran Shaghaghi - manuscript
    Physical systems can store information and their informational properties are governed by the laws of information. In particular, the amount of information that a physical system can convey is limited by the number of its degrees of freedom and their distinguishable states. Here we explore the properties of the physical systems with absolutely one degree of freedom. The central point in these systems is the tight limitation on their information capacity. Discussing the implications of this limitation (...)
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  22. An Expert System for Diagnosing Shortness of Breath in Infants and Children.Jihan Y. AbuEl-Reesh & Samy S. Abu-Naser - 2018 - International Journal of Engineering and Information Systems (IJEAIS) 1 (4):89-101.
    Background: With the coming of the Industrial Revolution, the levels of pollution grow significantly. This Technological development contributed to the worsening of shortness breath problems in great shape. especially in infants and children. There are many shortness breath diseases that infants and children face in their lives. Shortness of breath is one of a very serious symptom in children and infants and should never be ignored. Objectives: Along these lines, the main goal of this expert system is to help physician (...)
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  23. Complex Systems Biology.Roberto Serra - 2012 - In Vincenzo Fano, Enrico Giannetto, Giulia Giannini & Pierluigi Graziani (eds.), Complessità e Riduzionismo. ISONOMIA - Epistemologica Series Editor. pp. 100-107.
    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 (...)
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  24. How to Learn the Natural Numbers: Inductive Inference and the Acquisition of Number Concepts.Eric Margolis & Stephen Laurence - 2008 - Cognition 106 (2):924-939.
    Theories of number concepts often suppose that the natural numbers are acquired as children learn to count and as they draw an induction based on their interpretation of the first few count words. In a bold critique of this general approach, Rips, Asmuth, Bloomfield [Rips, L., Asmuth, J. & Bloomfield, A.. Giving the boot to the bootstrap: How not to learn the natural numbers. Cognition, 101, B51–B60.] argue that such an inductive inference is consistent with a representational system that (...)
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  25.  94
    The Physical Numbers: A New Foundational Logic-Numerical Structure For Mathematics And Physics.Gomez-Ramirez Danny A. J. - manuscript
    The boundless nature of the natural numbers imposes paradoxically a high formal bound to the use of standard artificial computer programs for solving conceptually challenged problems in number theory. In the context of the new cognitive foundations for mathematics' and physics' program immersed in the setting of artificial mathematical intelligence, we proposed a refined numerical system, called the physical numbers, preserving most of the essential intuitions of the natural numbers. Even more, this new numerical structure additionally possesses the property (...)
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  26. Knowledge-based systems that determine the appropriate students major: In the faculty of engineering and information technology.Samy S. Abu Naser & Ihab S. Zaqout - 2016 - World Wide Journal of Multidisciplinary Research and Development 2 (10):26-34.
    In this paper a Knowledge-Based System (KBS) for determining the appropriate students major according to his/her preferences for sophomore student enrolled in the Faculty of Engineering and Information Technology in Al-Azhar University of Gaza was developed and tested. A set of predefined criterions that is taken into consideration before a sophomore student can select a major is outlined. Such criterion as high school score, score of subject such as Math I, Math II, Electrical Circuit I, and Electronics I taken during (...)
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  27. The Sum of the Parts: Large-Scale Modeling in Systems Biology.Fridolin Gross & Sara Green - 2017 - Philosophy, Theory, and Practice in Biology 9 (10).
    Systems biologists often distance themselves from reductionist approaches and formulate their aim as understanding living systems “as a whole.” Yet, it is often unclear what kind of reductionism they have in mind, and in what sense their methodologies would offer a superior approach. To address these questions, we distinguish between two types of reductionism which we call “modular reductionism” and “bottom-up reductionism.” Much knowledge in molecular biology has been gained by decomposing living systems into functional modules or (...)
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  28. Neutosophic Quadruple Numbers, Refined Neutrosophic Quadruple Number, Absorbance Law, and the Multiplication of Neutrosophic Quadruple Numbers.Florentin Smarandache - 2015 - Neutrosophic Sets and Systems 10:96-98.
    In this paper, we introduce for the first time the neutrosophic quadruple numbers (of the form a + bT + cI + dF) and the refined neutrosophic quadruple numbers. Then we define an absorbance law, based on a prevalence order, both of them in order to multiply the neutrosophic components T, I, F, or their sub-components tJ, Ik, Fl and thus to construct the multiplication of neutrosophic quadruple numbers.
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  29. The Unified Medical Language System and the Gene Ontology: Some critical reflections.Anand Kumar & Barry Smith - 2003 - In A. Günter, R. Kruse & B. Neumann (eds.), KI 2003: Advances in Artificial Intelligence. Berlin: Springer. pp. 135-148.
    The Unified Medical Language System and the Gene Ontology are among the most widely used terminology resources in the biomedical domain. However, when we evaluate them in the light of simple principles for wellconstructed ontologies we find a number of characteristic inadequacies. Employing the theory of granular partitions, a new approach to the understanding of ontologies and of the relationships ontologies bear to instances in reality, we provide an application of this theory in relation to an example drawn from (...)
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  30. Indeterminism in Physics, Classical Chaos and Bohmian Mechanics: Are Real Numbers Really Real?Nicolas Gisin - 2019 - Erkenntnis (6):1-13.
    It is usual to identify initial conditions of classical dynamical systems with mathematical real numbers. However, almost all real numbers contain an infinite amount of information. I argue that a finite volume of space can’t contain more than a finite amount of information, hence that the mathematical real numbers are not physically relevant. Moreover, a better terminology for the so-called real numbers is “random numbers”, as their series of bits are truly random. I propose an alternative classical mechanics, which (...)
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  31. Some features of physical systems without time and dynamics (in English).Andrey Smirnov - manuscript
    Physical systems without time and dynamics have been considered. The principle of how to construct spacetime in a physical system without time and dynamics has been proposed. It has been found what can be objects in such a spacetime, and what can be an interaction between such objects. Within the framework of the considered class of systems, answers to the following problems of philosophy and physics have been found: the nature of consciousness and the connection of body and (...)
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  32. On Certain Axiomatizations of Arithmetic of Natural and Integer Numbers.Urszula Wybraniec-Skardowska - 2019 - Axioms 2019 (Deductive Systems).
    The systems of arithmetic discussed in this work are non-elementary theories. In this paper, natural numbers are characterized axiomatically in two di erent ways. We begin by recalling the classical set P of axioms of Peano’s arithmetic of natural numbers proposed in 1889 (including such primitive notions as: set of natural numbers, zero, successor of natural number) and compare it with the set W of axioms of this arithmetic (including the primitive notions like: set of natural numbers and (...)
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  33. Quantum behavior of the systems with a single degree of freedom and the derivation of quantum theory.Mehran Shaghaghi - manuscript
    The number of independent messages a physical system can carry is limited by the number of its adjustable properties. In particular, systems that have only one adjustable property cannot carry more than a single message at a time. We demonstrate this is the case for the single photons in the double-slit experiment, and the root of the fundamental limit on measuring the complementary aspect of the photons. Next, we analyze the other ‘quantal’ behavior of the systems (...)
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  34. Epistemic Limitations and Precise Estimates in Analog Magnitude Representation.Justin Halberda - 2016 - In A. Baron & D. Barner (eds.), Core Knowledge and Conceptual Change. Oxford University Press. pp. 167-186.
    This chapter presents a re-understanding of the contents of our analog magnitude representations (e.g., approximate duration, distance, number). The approximate number system (ANS) is considered, which supports numerical representations that are widely described as fuzzy, noisy, and limited in their representational power. The contention is made that these characterizations are largely based on misunderstandings—that what has been called “noise” and “fuzziness” is actually an important epistemic signal of confidence in one’s estimate of the value. Rather than the ANS (...)
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  35. Computation in Physical Systems: A Normative Mapping Account.Paul Schweizer - 2019 - In Matteo Vincenzo D'Alfonso & Don Berkich (eds.), On the Cognitive, Ethical, and Scientific Dimensions of Artificial Intelligence. Springer Verlag. pp. 27-47.
    The relationship between abstract formal procedures and the activities of actual physical systems has proved to be surprisingly subtle and controversial, and there are a number of competing accounts of when a physical system can be properly said to implement a mathematical formalism and hence perform a computation. I defend an account wherein computational descriptions of physical systems are high-level normative interpretations motivated by our pragmatic concerns. Furthermore, the criteria of utility and success vary according to our (...)
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  36.  29
    The Connectedness Illusion Influences Numerical Perception Throughout Development.Sam Clarke, Chuyan Qu, Francesca Luzzi & Elizabeth Brannon - manuscript
    Visual illusions of number provide a means of investigating the rules and principles through which approximate number representations are formed. Here, we investigated the developmental trajectory of an important numerical illusion – the connectedness illusion, wherein connecting pairs of items with thin lines reduces their perceived number without altering continuous attributes of the collections. We found that children as young as 5 years of age are affected by the illusion and that the magnitude of the effect increased (...)
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  37. Putting a number on the harm of death.Joseph Millum - 2019 - In Espen Gamlund & Carl Tollef Solberg (eds.), Saving People from the Harm of Death. New York: Oxford University Press. pp. 61-75.
    Donors to global health programs and policymakers within national health systems have to make difficult decisions about how to allocate scarce health care resources. Principled ways to make these decisions all make some use of summary measures of health, which provide a common measure of the value (or disvalue) of morbidity and mortality. They thereby allow comparisons between health interventions with different effects on the patterns of death and ill health within a population. The construction of a summary measure (...)
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  38. Exact equality and successor function: Two key concepts on the path towards understanding exact numbers.Véronique Izard, Pierre Pica, Elizabeth S. Spelke & Stanislas Dehaene - 2008 - Philosophical Psychology 21 (4):491 – 505.
    Humans possess two nonverbal systems capable of representing numbers, both limited in their representational power: the first one represents numbers in an approximate fashion, and the second one conveys information about small numbers only. Conception of exact large numbers has therefore been thought to arise from the manipulation of exact numerical symbols. Here, we focus on two fundamental properties of the exact numbers as prerequisites to the concept of EXACT NUMBERS : the fact that all numbers can be generated (...)
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  39. Analysis of minimal complex systems and complex problem solving require different forms of causal cognition.Joachim Funke - 2014 - Frontiers in Psychology 5.
    In the last 20 years, a stream of research emerged under the label of „complex problem solving“ (CPS). This research was intended to describe the way people deal with complex, dynamic, and intransparent situations. Complex computer-simulated scenarios were as stimulus material in psychological experiments. This line of research lead to subtle insights into the way how people deal with complexity and uncertainty. Besides these knowledge-rich, realistic, intransparent, complex, dynamic scenarios with many variables, a second line of research used more simple, (...)
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  40. Inverse Operations with Transfinite Numbers and the Kalam Cosmological Argument.Graham Oppy - 1995 - International Philosophical Quarterly 35 (2):219-221.
    William Lane Craig has argued that there cannot be actual infinities because inverse operations are not well-defined for infinities. I point out that, in fact, there are mathematical systems in which inverse operations for infinities are well-defined. In particular, the theory introduced in John Conway's *On Numbers and Games* yields a well-defined field that includes all of Cantor's transfinite numbers.
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  41. Organisations as Computing Systems.David Strohmaier - 2020 - Journal of Social Ontology 6 (2):211-236.
    Organisations are computing systems. The university’s sports centre is a computing system for managing sports teams and facilities. The tenure committee is a computing system for assigning tenure status. Despite an increasing number of publications in group ontology, the computational nature of organisations has not been recognised. The present paper is the first in this debate to propose a theory of organisations as groups structured for computing. I begin by describing the current situation in group ontology and by (...)
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  42. The material origin of numbers: Insights from the archaeology of the Ancient Near East.Karenleigh Anne Overmann - 2019 - Piscataway, NJ 08854, USA: Gorgias Press.
    What are numbers, and where do they come from? A novel answer to these timeless questions is proposed by cognitive archaeologist Karenleigh A. Overmann, based on her groundbreaking study of material devices used for counting in the Ancient Near East—fingers, tallies, tokens, and numerical notations—as interpreted through the latest neuropsychological insights into human numeracy and literacy. The result, a unique synthesis of interdisciplinary data, outlines how number concepts would have been realized in a pristine original condition to develop into (...)
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  43. Counting systems and the First Hilbert problem.Yaroslav Sergeyev - 2010 - Nonlinear Analysis Series A 72 (3-4):1701-1708.
    The First Hilbert problem is studied in this paper by applying two instruments: a new methodology distinguishing between mathematical objects and mathematical languages used to describe these objects; and a new numeral system allowing one to express different infinite numbers and to use these numbers for measuring infinite sets. Several counting systems are taken into consideration. It is emphasized in the paper that different mathematical languages can describe mathematical objects (in particular, sets and the number of their elements) (...)
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  44. Stability of sociopolitical systems in the context of globalization: revolution and democracy.Leonid Grinin & Andrey V. Korotayev - 2015 - Central European Journal of International and Security Studies 9 (2):01-34.
    Issues of sociopolitical systems’ stability and risks of their destabi-lization in process of political transformations belong to the most important ones as regards the social development perspectives, as has been shown again by the recent events in Ukraine. In this re-spect it appears necessary to note that the transition to democracy may pose a serious threat to the stability of respective sociopolitical systems. This article studies the issue of democratization of countries within globalization context, it points to the (...)
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  45.  80
    Foundation of Appurtenance and Inclusion Equations for Constructing the Operations of Neutrosophic Numbers Needed in Neutrosophic Statistics Foundation of Appurtenance and Inclusion Equations for Constructing the Operations of Neutrosophic Numbers Needed in Neutrosophic Statistics.Florentin Smarandache - 2024 - Neutrosophic Systems with Applications 15.
    We introduce for the first time the appurtenance equation and inclusion equation, which help in understanding the operations with neutrosophic numbers within the frame of neutrosophic statistics. The way of solving them resembles the equations whose coefficients are sets (not single numbers).
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  46. The SignalGlyph Project and Prime Numbers.Michael Joseph Winkler - 2021 - In Michael Winkler (ed.), The Image of Language. Northeast, NY: Artists Books Editions. pp. 158-163.
    An excerpt of "The SignalGlyph Project and Prime Numbers" (a chapter of the book THE IMAGE OF LANGUAGE) that attempts to illustrate how dimensional limitations of mathematical language have obscured recognition of the system of patterning in the distribution of prime numbers.
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  47. Lower and Upper Estimates of the Quantity of Algebraic Numbers.Yaroslav Sergeyev - 2023 - Mediterranian Journal of Mathematics 20:12.
    It is well known that the set of algebraic numbers (let us call it A) is countable. In this paper, instead of the usage of the classical terminology of cardinals proposed by Cantor, a recently introduced methodology using ①-based infinite numbers is applied to measure the set A (where the number ① is called grossone). Our interest to this methodology is explained by the fact that in certain cases where cardinals allow one to say only whether a set is (...)
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  48. Indeterminism in Physics, Classical Chaos and Bohmian Mechanics: Are Real Numbers Really Real?Nicolas Gisin - 2019 - Erkenntnis 86 (6):1469-1481.
    It is usual to identify initial conditions of classical dynamical systems with mathematical real numbers. However, almost all real numbers contain an infinite amount of information. I argue that a finite volume of space can’t contain more than a finite amount of information, hence that the mathematical real numbers are not physically relevant. Moreover, a better terminology for the so-called real numbers is “random numbers”, as their series of bits are truly random. I propose an alternative classical mechanics, which (...)
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  49. The Requirements of Computerized Management Information Systems and Their Role in Improving the Quality of Administrative Decisions in the Palestinian Ministry of Education and Higher Education.Mazen J. Al Shobaki & Samy S. Abu-Naser - 2017 - International Journal of Information Technology and Electrical Engineering 6 (6):7-35.
    The purpose of this study is to identify the requirements of computerized Management Information Systems and their role in improving the quality of administrative decisions in the Palestinian Ministry of Education and Higher Education. The authors used the descriptive analytical method and the questionnaire method to collect the data. (247) questionnaires were distributed on the study sample and (175) questionnaires were collected back with a recovery rate of (70.8). The study showed a number of results, the most important (...)
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  50. Everyday Deeds: Enactive Protest, Exit, and Silence in Deliberative Systems.Toby Rollo - 2017 - Political Theory 45 (5):587-609.
    The deliberative systems approach is a recent innovation within the tradition of deliberative democratic theory. It signals an important shift in focus from the political legitimacy produced within isolated and formal sites of deliberation (e.g., Parliament or deliberative mini-publics), to the legitimacy produced by a number of diverse interconnected sites. In this respect, the deliberative systems (DS) approach is better equipped to identify and address defects arising from the systemic influences of power and coercion. In this article, (...)
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