Results for 'Mathematics'

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  1. Mathematics Intelligent Tutoring System.Nour N. AbuEloun & Samy S. Abu Naser - 2017 - International Journal of Advanced Scientific Research 2 (1):11-16.
    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 (...)
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  2. Mathematical Monsters.Andrew Aberdein - 2019 - In Diego Compagna & Stefanie Steinhart (eds.), Monsters, Monstrosities, and the Monstrous in Culture and Society. Wilmington, DE, USA: pp. 391-412.
    Monsters lurk within mathematical as well as literary haunts. I propose to trace some pathways between these two monstrous habitats. I start from Jeffrey Jerome Cohen’s influential account of monster culture and explore how well mathematical monsters fit each of his seven theses. The mathematical monsters I discuss are drawn primarily from three distinct but overlapping domains. Firstly, late nineteenth-century mathematicians made numerous unsettling discoveries that threatened their understanding of their own discipline and challenged their intuitions. The great French mathematician (...)
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  3. Mathematics as language.Adam Morton - 1996 - In Adam Morton & Stephen P. Stich (eds.), Benacerraf and His Critics. Blackwell. pp. 213--227.
    I discuss ways in which the linguistic form of mathimatics helps us think mathematically.
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  4. Mathematics - an imagined tool for rational cognition.Boris Culina - manuscript
    Analysing several characteristic mathematical models: natural and real numbers, Euclidean geometry, group theory, and set theory, I argue that a mathematical model in its final form is a junction of a set of axioms and an internal partial interpretation of the corresponding language. It follows from the analysis that (i) mathematical objects do not exist in the external world: they are our internally imagined objects, some of which, at least approximately, we can realize or represent; (ii) mathematical truths are not (...)
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  5. The Principles of Mathematics.Bertrand Russell - 1903 - Cambridge, England: Allen & Unwin.
    Published in 1903, this book was the first comprehensive treatise on the logical foundations of mathematics written in English. It sets forth, as far as possible without mathematical and logical symbolism, the grounds in favour of the view that mathematics and logic are identical. It proposes simply that what is commonly called mathematics are merely later deductions from logical premises. It provided the thesis for which _Principia Mathematica_ provided the detailed proof, and introduced the work of Frege (...)
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  6. Mathematical Knowledge, the Analytic Method, and Naturalism.Fabio Sterpetti - 2018 - In Sorin Bangu (ed.), Naturalizing Logico-Mathematical Knowledge. Approaches from Philosophy, Psychology and Cognitive Science. New York, Stati Uniti: pp. 268-293.
    This chapter tries to answer the following question: How should we conceive of the method of mathematics, if we take a naturalist stance? The problem arises since mathematical knowledge is regarded as the paradigm of certain knowledge, because mathematics is based on the axiomatic method. Moreover, natural science is deeply mathematized, and science is crucial for any naturalist perspective. But mathematics seems to provide a counterexample both to methodological and ontological naturalism. To face this problem, some authors (...)
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  7. Mathematical Modelling and Contrastive Explanation.Adam Morton - 1990 - Canadian Journal of Philosophy 20 (Supplement):251-270.
    Mathematical models provide explanations of limited power of specific aspects of phenomena. One way of articulating their limits here, without denying their essential powers, is in terms of contrastive explanation.
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  8. Mathematical Gettier Cases and Their Implications.Neil Barton - manuscript
    Let mathematical justification be the kind of justification obtained when a mathematician provides a proof of a theorem. Are Gettier cases possible for this kind of justification? At first sight we might think not: The standard for mathematical justification is proof and, since proof is bound at the hip with truth, there is no possibility of having an epistemically lucky justification of a true mathematical proposition. In this paper, I argue that Gettier cases are possible (and indeed actual) in mathematical (...)
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  9. Mathematical Explanations and the Piecemeal Approach to Thinking About Explanation.Gabriel Târziu - 2018 - Logique Et Analyse 61 (244):457-487.
    A new trend in the philosophical literature on scientific explanation is that of starting from a case that has been somehow identified as an explanation and then proceed to bringing to light its characteristic features and to constructing an account for the type of explanation it exemplifies. A type of this approach to thinking about explanation – the piecemeal approach, as I will call it – is used, among others, by Lange (2013) and Pincock (2015) in the context of their (...)
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  10. From Mathematical Fictionalism to Truth‐Theoretic Fictionalism.Bradley Armour-Garb & James A. Woodbridge - 2014 - Philosophy and Phenomenological Research 88 (1):93-118.
    We argue that if Stephen Yablo (2005) is right that philosophers of mathematics ought to endorse a fictionalist view of number-talk, then there is a compelling reason for deflationists about truth to endorse a fictionalist view of truth-talk. More specifically, our claim will be that, for deflationists about truth, Yablo’s argument for mathematical fictionalism can be employed and mounted as an argument for truth-theoretic fictionalism.
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  11.  93
    Mathematical Thinking Undefended on The Level of The Semester for Professional Mathematics Teacher Candidates. Toheri & Widodo Winarso - 2017 - Munich University Library.
    Mathematical thinking skills are very important in mathematics, both to learn math or as learning goals. Thinking skills can be seen from the description given answers in solving mathematical problems faced. Mathematical thinking skills can be seen from the types, levels, and process. Proportionally questions given to students at universities in Indonesia (semester I, III, V, and VII). These questions are a matter of description that belong to the higher-level thinking. Students choose 5 of 8 given problem. Qualitatively, the (...)
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  12. Mathematical Cognition: A Case of Enculturation.Richard Menary - 2015 - Open Mind.
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  13.  88
    Innate Mathematical Characteristics and Number Sense Competencies of Junior High School Students.Raymundo A. Santos, Leila M. Collantes, Edwin D. Ibañez, Florante P. Ibarra & Jupeth Pentang - 2022 - International Journal of Learning, Teaching and Educational Research 21 (10):325-340.
    The study determined the influence of innate mathematical characteristics on the number sense competencies of junior high school students in a Philippine public school. The descriptive-correlational research design was used to accomplish the study involving a nonrandom sample of sixty 7th-grade students attending synchronous math sessions. Data obtained from the math-specific Learning Style and Self-Efficacy questionnaires and the modified Number Sense Test (NST) were analyzed and interpreted using descriptive statistics, Pearson’s Chi-Square, and Simple Linear Regression analysis. The research instruments and (...)
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  14. Mathematical shortcomings in a simulated universe.Samuel Alexander - 2018 - The Reasoner 12 (9):71-72.
    I present an argument that for any computer-simulated civilization we design, the mathematical knowledge recorded by that civilization has one of two limitations. It is untrustworthy, or it is weaker than our own mathematical knowledge. This is paradoxical because it seems that nothing prevents us from building in all sorts of advantages for the inhabitants of said simulation.
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  15. Mathematics and argumentation.Andrew Aberdein - 2009 - Foundations of Science 14 (1-2):1-8.
    Some authors have begun to appeal directly to studies of argumentation in their analyses of mathematical practice. These include researchers from an impressively diverse range of disciplines: not only philosophy of mathematics and argumentation theory, but also psychology, education, and computer science. This introduction provides some background to their work.
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  16. Mathematical Metaphors in Natorp’s Neo-Kantian Epistemology and Philosophy of Science.Thomas Mormann - 2005 - In Falk Seeger, Johannes Lenard & Michael H. G. Hoffmann (eds.), Activity and Sign. Grounding Mathematical Education. Springer.
    A basic thesis of Neokantian epistemology and philosophy of science contends that the knowing subject and the object to be known are only abstractions. What really exists, is the relation between both. For the elucidation of this “knowledge relation ("Erkenntnisrelation") the Neokantians of the Marburg school used a variety of mathematical metaphors. In this con-tribution I reconsider some of these metaphors proposed by Paul Natorp, who was one of the leading members of the Marburg school. It is shown that Natorp's (...)
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  17.  56
    Mathematical Needs of Laura Vicuña Learners.Jupeth Pentang, Ronalyn M. Bautista, Aylene D. Pizaña & Susana P. Egger - 2020 - WPU Graduate Journal 5 (1):78-81.
    An inquiry on the training needs in Mathematics was conducted to Laura Vicuña Center - Palawan (LVC-P) learners. Specifically, this aimed to determine their level of performance in numbers, measurement, geometry, algebra, and statistics, identify the difficulties they encountered in solving word problems and enumerate topics where they needed coaching. -/- To identify specific training needs, the study employed a descriptive research design where 36 participants were sampled purposively. The data were gathered through a problem set test and focus (...)
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  18. Mathematical skepticism: a sketch with historian in foreground.Luciano Floridi - 1998 - In J. van der Zande & R. Popkin (eds.), The Skeptical Tradition around 1800. Dordrecht, Netherlands: pp. 41–60.
    We know very little about mathematical skepticism in modem times. Imre Lakatos once remarked that “in discussing modem efforts to establish foundations for mathematical knowledge one tends to forget that these are but a chapter in the great effort to overcome skepticism by establishing foundations for knowledge in general." And in a sense he was clearly right: modem thought — with its new discoveries in mathematical sciences, the mathematization of physics, the spreading of Pyrrhonist doctrines, the centrality of epistemological foundationalism (...)
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  19. Mathematical biology and the existence of biological laws.Mauro Dorato - 2012 - In D. Dieks, S. Hartmann, T. Uebel & M. Weber (eds.), Probabilities, Laws and Structure. Springer.
    An influential position in the philosophy of biology claims that there are no biological laws, since any apparently biological generalization is either too accidental, fact-like or contingent to be named a law, or is simply reducible to physical laws that regulate electrical and chemical interactions taking place between merely physical systems. In the following I will stress a neglected aspect of the debate that emerges directly from the growing importance of mathematical models of biological phenomena. My main aim is to (...)
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  20. Mathematical Models of Abstract Systems: Knowing abstract geometric forms.Jean-Pierre Marquis - 2013 - Annales de la Faculté des Sciences de Toulouse 22 (5):969-1016.
    Scientists use models to know the world. It i susually assumed that mathematicians doing pure mathematics do not. Mathematicians doing pure mathematics prove theorems about mathematical entities like sets, numbers, geometric figures, spaces, etc., they compute various functions and solve equations. In this paper, I want to exhibit models build by mathematicians to study the fundamental components of spaces and, more generally, of mathematical forms. I focus on one area of mathematics where models occupy a central role, (...)
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  21. Mathematics, core of the past and hope of the future.James Franklin - 2018 - In Catherine A. Runcie & David Brooks (eds.), Reclaiming Education: Renewing Schools and Universities in Contemporary Western Society. Sydney, Australia: Edwin H. Lowe Publishing. pp. 149-162.
    Mathematics has always been a core part of western education, from the medieval quadrivium to the large amount of arithmetic and algebra still compulsory in high schools. It is an essential part. Its commitment to exactitude and to rigid demonstration balances humanist subjects devoted to appreciation and rhetoric as well as giving the lie to postmodernist insinuations that all “truths” are subject to political negotiation. In recent decades, the character of mathematics has changed – or rather broadened: it (...)
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  22. Mathematics, Morality, and Self‐Effacement.Jack Woods - 2016 - Noûs.
    I argue that certain species of belief, such as mathematical, logical, and normative beliefs, are insulated from a form of Harman-style debunking argument whereas moral beliefs, the primary target of such arguments, are not. Harman-style arguments have been misunderstood as attempts to directly undermine our moral beliefs. They are rather best given as burden-shifting arguments, concluding that we need additional reasons to maintain our moral beliefs. If we understand them this way, then we can see why moral beliefs are vulnerable (...)
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  23. Mathematical Deduction by Induction.Christy Ailman - 2013 - Gratia Eruditionis:4-12.
    In attempt to provide an answer to the question of origin of deductive proofs, I argue that Aristotle’s philosophy of math is more accurate opposed to a Platonic philosophy of math, given the evidence of how mathematics began. Aristotle says that mathematical knowledge is a posteriori, known through induction; but once knowledge has become unqualified it can grow into deduction. Two pieces of recent scholarship on Greek mathematics propose new ways of thinking about how mathematics began in (...)
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  24. Wisdom Mathematics.Nicholas Maxwell - 2010 - Friends of Wisdom Newsletter (6):1-6.
    For over thirty years I have argued that all branches of science and scholarship would have both their intellectual and humanitarian value enhanced if pursued in accordance with the edicts of wisdom-inquiry rather than knowledge-inquiry. I argue that this is true of mathematics. Viewed from the perspective of knowledge-inquiry, mathematics confronts us with two fundamental problems. (1) How can mathematics be held to be a branch of knowledge, in view of the difficulties that view engenders? What could (...)
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  25. Leibniz, Mathematics and the Monad.Simon Duffy - 2010 - In Sjoerd van Tuinen & Niamh McDonnell (eds.), Deleuze and the Fold: A Critical Reader. Palgrave-Macmillan. pp. 89--111.
    The reconstruction of Leibniz’s metaphysics that Deleuze undertakes in The Fold provides a systematic account of the structure of Leibniz’s metaphysics in terms of its mathematical foundations. However, in doing so, Deleuze draws not only upon the mathematics developed by Leibniz—including the law of continuity as reflected in the calculus of infinite series and the infinitesimal calculus—but also upon developments in mathematics made by a number of Leibniz’s contemporaries—including Newton’s method of fluxions. He also draws upon a number (...)
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  26.  36
    Gödel mathematics versus Hilbert mathematics. I. The Gödel incompleteness (1931) statement: axiom or theorem?Vasil Penchev - 2022 - Logic and Philosophy of Mathematics eJournal (Elsevier: SSRN) 14 (9):1-56.
    The present first part about the eventual completeness of mathematics (called “Hilbert mathematics”) is concentrated on the Gödel incompleteness (1931) statement: if it is an axiom rather than a theorem inferable from the axioms of (Peano) arithmetic, (ZFC) set theory, and propositional logic, this would pioneer the pathway to Hilbert mathematics. One of the main arguments that it is an axiom consists in the direct contradiction of the axiom of induction in arithmetic and the axiom of infinity (...)
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  27. Virtual Mathematics: the logic of difference.Simon Duffy (ed.) - 2006 - Clinamen.
    Of all twentieth century philosophers, it is Gilles Deleuze whose work agitates most forcefully for a worldview privileging becoming over being, difference over sameness; the world as a complex, open set of multiplicities. Nevertheless, Deleuze remains singular in enlisting mathematical resources to underpin and inform such a position, refusing the hackneyed opposition between ‘static’ mathematical logic versus ‘dynamic’ physical world. This is an international collection of work commissioned from foremost philosophers, mathematicians and philosophers of science, to address the wide range (...)
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  28. Mathematical Modality: An Investigation of Set Theoretic Contingency.Andrew Bacon -
    An increasing amount of contemporary philosophy of mathematics posits, and theorizes in terms of special kinds of mathematical modality. The goal of this paper is to bring recent work on higher-order metaphysics to bear on the investigation of these modalities. -/- The main focus of the paper will be views that posit mathematical contingency or indeterminacy about statements that concern the `width' of the set theoretic universe, such as Cantor's continuum hypothesis. In the higher-order framework I show that contingency (...)
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  29.  68
    Mathematics, isomorphism, and the identity of objects.Graham White - 2021 - Journal of Knowledge Structures and Systems 2 (2):56-58.
    We compare the medieval projects of commentaries and disputations with the modern projects of formal ontology and of mathematics.
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  30. A Mathematical Model of Divine Infinity.Eric Steinhart - 2009 - Theology and Science 7 (3):261-274.
    Mathematics is obviously important in the sciences. And so it is likely to be equally important in any effort that aims to understand God in a scientifically significant way or that aims to clarify the relations between science and theology. The degree to which God has any perfection is absolutely infinite. We use contemporary mathematics to precisely define that absolute infinity. For any perfection, we use transfinite recursion to define an endlessly ascending series of degrees of that perfection. (...)
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  31. Mathematics and Explanatory Generality: Nothing but Cognitive Salience.Juha Saatsi & Robert Knowles - 2021 - Erkenntnis 86 (5):1119-1137.
    We demonstrate how real progress can be made in the debate surrounding the enhanced indispensability argument. Drawing on a counterfactual theory of explanation, well-motivated independently of the debate, we provide a novel analysis of ‘explanatory generality’ and how mathematics is involved in its procurement. On our analysis, mathematics’ sole explanatory contribution to the procurement of explanatory generality is to make counterfactual information about physical dependencies easier to grasp and reason with for creatures like us. This gives precise content (...)
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  32. Mathematical symbols as epistemic actions.Johan De Smedt & Helen De Cruz - 2013 - Synthese 190 (1):3-19.
    Recent experimental evidence from developmental psychology and cognitive neuroscience indicates that humans are equipped with unlearned elementary mathematical skills. However, formal mathematics has properties that cannot be reduced to these elementary cognitive capacities. The question then arises how human beings cognitively deal with more advanced mathematical ideas. This paper draws on the extended mind thesis to suggest that mathematical symbols enable us to delegate some mathematical operations to the external environment. In this view, mathematical symbols are not only used (...)
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  33.  91
    Non-mathematical Content by Mathematical Means.Sam Adam-Day - manuscript
    In this paper, I consider the use of mathematical results in philosophical arguments arriving at conclusions with non-mathematical content, with the view that in general such usage requires additional justification. As a cautionary example, I examine Kreisel’s arguments that the Continuum Hypothesis is determined by the axioms of Zermelo-Fraenkel set theory, and interpret Weston’s 1976 reply as showing that Kreisel fails to provide sufficient justification for the use of his main technical result. If we take the perspective that mathematical results (...)
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  34.  24
    Alternative mathematics and alternative theoretical physics: The method for linking them together.Antonino Drago - 1996 - Epistemologia 19 (1):33-50.
    I characterize Bishop's constructive mathematics as an alternative to classical mathematics, which makes use of the actual infinity. From the history an accurate investigation of past physical theories I obtianed some ones - mainly Lazare Carnot's mechanics and Sadi Carnot's thermodynamics - which are alternative to the dominant theories - e.g. Newtopn's mechanics. The way to link together mathematics to theoretical physics is generalized and some general considerations, in particualr on the geoemtry in theoretical physics, are obtained.that.
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  35. Mathematical Explanation by Law.Sam Baron - 2019 - British Journal for the Philosophy of Science 70 (3):683-717.
    Call an explanation in which a non-mathematical fact is explained—in part or in whole—by mathematical facts: an extra-mathematical explanation. Such explanations have attracted a great deal of interest recently in arguments over mathematical realism. In this article, a theory of extra-mathematical explanation is developed. The theory is modelled on a deductive-nomological theory of scientific explanation. A basic DN account of extra-mathematical explanation is proposed and then redeveloped in the light of two difficulties that the basic theory faces. The final view (...)
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  36. Mathematical Wit and Mathematical Cognition.Andrew Aberdein - 2013 - Topics in Cognitive Science 5 (2):231-250.
    The published works of scientists often conceal the cognitive processes that led to their results. Scholars of mathematical practice must therefore seek out less obvious sources. This article analyzes a widely circulated mathematical joke, comprising a list of spurious proof types. An account is proposed in terms of argumentation schemes: stereotypical patterns of reasoning, which may be accompanied by critical questions itemizing possible lines of defeat. It is argued that humor is associated with risky forms of inference, which are essential (...)
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  37. Mathematics as Make-Believe: A Constructive Empiricist Account.Sarah Elizabeth Hoffman - 1999 - Dissertation, University of Alberta (Canada)
    Any philosophy of science ought to have something to say about the nature of mathematics, especially an account like constructive empiricism in which mathematical concepts like model and isomorphism play a central role. This thesis is a contribution to the larger project of formulating a constructive empiricist account of mathematics. The philosophy of mathematics developed is fictionalist, with an anti-realist metaphysics. In the thesis, van Fraassen's constructive empiricism is defended and various accounts of mathematics are considered (...)
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  38. Mathematical Platonism.Massimo Pigliucci - 2011 - Philosophy Now 84:47-47.
    Are numbers and other mathematical objects "out there" in some philosophically meaningful sense?
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  39. Mathematical Modeling in Biology: Philosophy and Pragmatics.Rasmus Grønfeldt Winther - 2012 - Frontiers in Plant Evolution and Development 2012:1-3.
    Philosophy can shed light on mathematical modeling and the juxtaposition of modeling and empirical data. This paper explores three philosophical traditions of the structure of scientific theory—Syntactic, Semantic, and Pragmatic—to show that each illuminates mathematical modeling. The Pragmatic View identifies four critical functions of mathematical modeling: (1) unification of both models and data, (2) model fitting to data, (3) mechanism identification accounting for observation, and (4) prediction of future observations. Such facets are explored using a recent exchange between two groups (...)
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  40. When mathematics touches physics: Henri Poincaré on probability.Jacintho Del Vecchio Junior - manuscript
    Probability plays a crucial role regarding the understanding of the relationship which exists between mathematics and physics. It will be the point of departure of this brief reflection concerning this subject, as well as about the placement of Poincaré’s thought in the scenario offered by some contemporary perspectives.
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  41. Review – Mathematical Doodlings. [REVIEW]Karl Pfeifer - 2017 - Metapsychology Online Reviews 21 (45):n.p..
    A review of Geoffrey Marnell, Mathematical Doodlings: Curiosities, conjectures, and challenges.
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  42. The Mathematical Theory of Categories in Biology and the Concept of Natural Equivalence in Robert Rosen.Franck Varenne - 2013 - Revue d'Histoire des Sciences 66 (1):167-197.
    The aim of this paper is to describe and analyze the epistemological justification of a proposal initially made by the biomathematician Robert Rosen in 1958. In this theoretical proposal, Rosen suggests using the mathematical concept of “category” and the correlative concept of “natural equivalence” in mathematical modeling applied to living beings. Our questions are the following: According to Rosen, to what extent does the mathematical notion of category give access to more “natural” formalisms in the modeling of living beings? Is (...)
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  43. Rejecting Mathematical Realism while Accepting Interactive Realism.Seungbae Park - 2018 - Analysis and Metaphysics 17:7-21.
    Indispensablists contend that accepting scientific realism while rejecting mathematical realism involves a double standard. I refute this contention by developing an enhanced version of scientific realism, which I call interactive realism. It holds that interactively successful theories are typically approximately true, and that the interactive unobservable entities posited by them are likely to exist. It is immune to the pessimistic induction while mathematical realism is susceptible to it.
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  44.  42
    Traditional Mathematics Is Not the Language of Nature: Multivalued Interaction Dynamics Makes the World Go Round.Andrei P. Kirilyuk -
    We show that critically accumulating "difficult" problems, contradictions and stagnation in modern science have the unified and well-specified mathematical origin in the explicit, artificial reduction of any interaction problem solution to an "exact", dynamically single-valued (or unitary) function, while in reality any unreduced interaction development leads to a dynamically multivalued solution describing many incompatible system configurations, or "realisations", that permanently replace one another in causally random order. We obtain thus the universal concept of dynamic complexity and chaos impossible in unitary (...)
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  45. Mathematical Structure of the Emergent Event.Kent Palmer - manuscript
    Exploration of a hypothetical model of the structure of the Emergent Event. -/- Key Words: Emergent Event, Foundational Mathematical Categories, Emergent Meta-system, Orthogonal Centering Dialectic, Hegel, Sartre, Badiou, Derrida, Deleuze, Philosophy of Science.
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  46. Mathematics, explanation and reductionism: exposing the roots of the Egyptianism of European civilization.Arran Gare - 2005 - Cosmos and History 1 (1):54-89.
    We have reached the peculiar situation where the advance of mainstream science has required us to dismiss as unreal our own existence as free, creative agents, the very condition of there being science at all. Efforts to free science from this dead-end and to give a place to creative becoming in the world have been hampered by unexamined assumptions about what science should be, assumptions which presuppose that if creative becoming is explained, it will be explained away as an illusion. (...)
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  47.  35
    Mathematical and Non-causal Explanations: an Introduction.Daniel Kostić - 2019 - Perspectives on Science 1 (27):1-6.
    In the last couple of years, a few seemingly independent debates on scientific explanation have emerged, with several key questions that take different forms in different areas. For example, the questions what makes an explanation distinctly mathematical and are there any non-causal explanations in sciences (i.e., explanations that don’t cite causes in the explanans) sometimes take a form of the question of what makes mathematical models explanatory, especially whether highly idealized models in science can be explanatory and in virtue of (...)
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  48. Mathematical thought in the light of Matte Blanco’s work.Giuseppe Iurato - 2013 - Philosophy of Mathematics Education Journal 27:1-9.
    Taking into account some basic epistemological considerations on psychoanalysis by Ignacio Matte Blanco, it is possible to deduce some first simple remarks on certain logical aspects of schizophrenic reasoning. Further remarks on mathematical thought are also made in the light of what established, taking into account the comparison with the schizophrenia pattern.
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  49. Mathematical Modeling of Biological and Social Evolutionary Macrotrends.Leonid Grinin, Alexander V. Markov & Andrey V. Korotayev - 2014 - In History & Mathematics: Trends and Cycles. Volgograd,Russia: Uchitel Publishing House. pp. 9-48.
    In the first part of this article we survey general similarities and differences between biological and social macroevolution. In the second (and main) part, we consider a concrete mathematical model capable of describing important features of both biological and social macroevolution. In mathematical models of historical macrodynamics, a hyperbolic pattern of world population growth arises from non-linear, second-order positive feedback between demographic growth and technological development. Based on diverse paleontological data and an analogy with macrosociological models, we suggest that the (...)
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  50. History & Mathematics: Trends and Cycles.Leonid Grinin & Andrey V. Korotayev - 2014 - Volgograd: "Uchitel" Publishing House.
    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 (...)
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