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Journal articles on the topic 'Tall's worlds of mathematics'

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Author: Grafiati

Published: 10 December 2022

Last updated: 28 January 2023

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1

Paz, Tamar, and Uri Leron. "The Slippery Road From Actions on Objects to Functions and Variables." Journal for Research in Mathematics Education 40, no. 1 (January 2009): 18–39. http://dx.doi.org/10.5951/jresematheduc.40.1.0018.

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Functions are all around us, disguised as actions on concrete objects. Composition of functions, too, is all around us, because these actions can be performed in succession, the output of one serving as the input for the next. In terms of Gray and Tall's (2001) “embodied objects” or Lakoff and Núñez's (2000) “mathematical idea analysis,” this “embodied scheme” of action on objects may serve as intuitive grounding for the function concept. However, as Gray, Tall, and their colleagues have shown, such embodied schemes can also lead to serious “epistemological obstacles” in later stages of concept development. In the same vein, our own data show that the intuitions about change and invariance entailed by the action-on-objects scheme, although helpful in earlier stages of learning functions, may later come to clash with the formal concepts of function and of composition of functions.

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2

Gouvea, F. Q. "MATHEMATICS: Parallel Worlds." Science 306, no. 5703 (December 10, 2004): 1893a—1894a. http://dx.doi.org/10.1126/science.1105298.

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3

Klaver, Elizabeth. "Possible Worlds, Mathematics, and John Mighton's Possible Worlds." Narrative 14, no. 1 (2006): 45–63. http://dx.doi.org/10.1353/nar.2005.0027.

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4

Rowe, David E. "Exotic worlds: Victorian mathematics." Metascience 22, no. 2 (October 9, 2012): 447–50. http://dx.doi.org/10.1007/s11016-012-9716-8.

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5

Apolloni, Bruno, Simone Bassis, and Dario Malchiodi. "Compatible worlds." Nonlinear Analysis: Theory, Methods & Applications 71, no. 12 (December 2009): e2883-e2901. http://dx.doi.org/10.1016/j.na.2009.06.104.

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6

Mancilla, Blanca, and John Plaice. "Possible Worlds Versioning." Mathematics in Computer Science 2, no. 1 (November 2008): 63–83. http://dx.doi.org/10.1007/s11786-008-0044-8.

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7

Maki, Daniel P., and John L. Casti. "Would-be Worlds." American Mathematical Monthly 105, no. 10 (December 1998): 972. http://dx.doi.org/10.2307/2589307.

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8

Barbour, A. D., and Gesine Reinert. "Small worlds." Random Structures and Algorithms 19, no. 1 (2001): 54–74. http://dx.doi.org/10.1002/rsa.1018.

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9

Pinheiro, M. R. "Medium worlds theories I." Applied Mathematics and Computation 188, no. 2 (May 2007): 1061–70. http://dx.doi.org/10.1016/j.amc.2006.05.213.

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10

AHMED, AFZAL. "Mathematics—A Tale of Three Worlds?" Teaching Mathematics and its Applications 14, no. 4 (1995): 141–48. http://dx.doi.org/10.1093/teamat/14.4.141.

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11

Barbour, A. D., and Gesine Reinert. "Correction: Small worlds." Random Structures and Algorithms 25, no. 1 (2004): 115. http://dx.doi.org/10.1002/rsa.20028.

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12

MOREIRA, CÅNDIDA QUEIROZ. "Between the Academic Mathematics and the Mathematics Education Worlds." European Journal of Teacher Education 20, no. 2 (January 1997): 171–89. http://dx.doi.org/10.1080/0261976970200206.

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13

Oh, Hee. "Euclidean Traveller in Hyperbolic Worlds." Notices of the American Mathematical Society 69, no. 11 (December 1, 2022): 1. http://dx.doi.org/10.1090/noti2579.

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14

Liljedahl, Peter, Nathalie Sinclair, and Rina Zazkis. "Number concepts withNumber Worlds: thickening understandings." International Journal of Mathematical Education in Science and Technology 37, no. 3 (April 15, 2006): 253–75. http://dx.doi.org/10.1080/00207390500285909.

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15

Esmonde, Indigo, and Jennifer M. Langer-Osuna. "Power in Numbers: Student Participation in Mathematical Discussions in Heterogeneous Spaces." Journal for Research in Mathematics Education 44, no. 1 (January 2013): 288–315. http://dx.doi.org/10.5951/jresematheduc.44.1.0288.

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In this article, mathematics classrooms are conceptualized as heterogeneous spaces in which multiple figured worlds come into contact. The study explores how a group of high school students drew upon several figured worlds as they navigated mathematical discussions. Results highlight 3 major points. First, the students drew on 2 primary figured worlds: a mathematics learning figured world and a figured world of friendship and romance. Both of these figured worlds were racialized and gendered, and were actively constructed and contested by the students. Second, these figured worlds offered resources for 1 African American student, Dawn, to position herself powerfully within classroom hierarchies. Third, these acts of positioning allowed Dawn to engage in mathematical practices such as conjecturing, clarifying ideas, and providing evidence.

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16

Berkovski, Sandy. "Possible Worlds: A Neo-Fregean Alternative." Axiomathes 21, no. 4 (March 6, 2010): 531–51. http://dx.doi.org/10.1007/s10516-010-9096-x.

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17

Hanson, Robin D. "Drift–diffusion in mangled worlds quantum mechanics." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 462, no. 2069 (February 21, 2006): 1619–27. http://dx.doi.org/10.1098/rspa.2005.1640.

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In Everett's many-worlds interpretation, where quantum measurements are seen as decoherence events, inexact decoherence may let large worlds mangle the memories of observers in small worlds, creating a cutoff in observable world measure. I solve a growth–drift–diffusion–absorption model of such a mangled worlds scenario, and show that it reproduces the Born probability rule closely, though not exactly. Thus, inexact decoherence may allow the Born rule to be derived in a many-worlds approach via world counting, using a finite number of worlds and no new fundamental physics.

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18

DE BERG, MARK, MARC VAN KREVELD, BENGT J. NILSSON, and MARK OVERMARS. "SHORTEST PATH QUERIES IN RECTILINEAR WORLDS." International Journal of Computational Geometry & Applications 02, no. 03 (September 1992): 287–309. http://dx.doi.org/10.1142/s0218195992000172.

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In this paper, a data structure is given for two and higher dimensional shortest path queries. For a set of n axis-parallel rectangles in the plane, or boxes in d-space, and a fixed target, it is possible with this structure to find a shortest rectilinear path avoiding all rectangles or boxes from any point to this target. Alternatively, it is possible to find the length of the path. The metric considered is a generalization of the L1-metric and the link metric, where the length of a path is its L1-length plus some (fixed) constant times the number of turns on the path. The data structure has size O((n log n)d−1), and a query takes O( log d−1 n) time (plus the output size if the path must be reported). As a byproduct, a relatively simple solution to the single shot problem is obtained; the shortest path between two given points can be computed in time O(nd log n) for d≥3, and in time O(n2) in the plane.

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19

Bellman, Kirstie L., and Christopher Landauer. "Virtual worlds as meeting places for formal systems." Applied Mathematics and Computation 120, no. 1-3 (May 2001): 165–73. http://dx.doi.org/10.1016/s0096-3003(99)00239-8.

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20

Kauffman, Louis H. "Non-Commutative Worlds and Relativity." Journal of Physics: Conference Series 2081, no. 1 (November 1, 2021): 012006. http://dx.doi.org/10.1088/1742-6596/2081/1/012006.

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Abstract This paper shows how aspects of gauge theory, Hamiltonian mechanics and quantum mechanics arise naturally in the mathematics of a non-commutative framework for calculus and differential geometry.

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21

Kauffman, Louis H. "Glafka-2004: Non-Commutative Worlds." International Journal of Theoretical Physics 45, no. 8 (September 6, 2006): 1439–66. http://dx.doi.org/10.1007/s10773-006-9201-5.

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22

Hoffmann, Miklós. "The Ontological Role of Applied Mathematics in Virtual Worlds." Philosophies 7, no. 1 (February 21, 2022): 22. http://dx.doi.org/10.3390/philosophies7010022.

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In this paper, I will argue that with the emergence of digital virtual worlds (in video games, animation movies, etc.) by the animation industry, we need to rethink the role and authority of mathematics, also from an ontological point of view. First I will demonstrate that the application of mathematics to the creation and description of the digital, virtual worlds behaves in many respects analogously to the application of mathematics to the description of real-world phenomena from the viewpoint of the history of science. However, from other aspects, the application of mathematics significantly differs in this virtual world from the application to real-world fields. The main thesis of my paper is that the role of mathematics in the digital animation industry can be ontologically different from its usual role. In the application of mathematics to digital virtual worlds, mathematical concepts are no longer just modelling tools, forming a subordinated, computational basis, but they can direct and organise, and even create non-mathematical theory, something that we can call, for example, digital physics and biology. I will study this new, creative role of mathematics through some concrete phenomena, specifically through gravity. Our conclusion is that the animation industry opens an entirely new chapter in the relationship between (digital) sciences and mathematics.

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23

Herzig, Abbe H. "Women Belonging in the Social Worlds of Graduate Mathematics." Mathematics Enthusiast 7, no. 2-3 (July 1, 2010): 177–208. http://dx.doi.org/10.54870/1551-3440.1183.

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24

Rzhetsky, Andrey, and James A. Evans. "War of Ontology Worlds: Mathematics, Computer Code, or Esperanto?" PLoS Computational Biology 7, no. 9 (September 29, 2011): e1002191. http://dx.doi.org/10.1371/journal.pcbi.1002191.

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25

SILLARI, GIACOMO. "QUANTIFIED LOGIC OF AWARENESS AND IMPOSSIBLE POSSIBLE WORLDS." Review of Symbolic Logic 1, no. 4 (December 2008): 514–29. http://dx.doi.org/10.1017/s1755020308090072.

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Among the many possible approaches to dealing with logical omniscience, I consider here awareness and impossible worlds structures. The former approach, pioneered by Fagin and Halpern, distinguishes between implicit and explicit knowledge, and avoids logical omniscience with respect to explicit knowledge. The latter, developed by Rantala and by Hintikka, allows for the existence of logically impossible worlds to which the agents are taken to have “epistemological” access; since such worlds need not behave consistently, the agents’ knowledge is fallible relative to logical omniscience. The two approaches are known to be equally expressive in propositional systems interpreted over Kripke semantics. In this paper I show that the two approaches are equally expressive in propositional systems interpreted over Montague-Scott (neighborhood) semantics. Furthermore, I provide predicate systems of both awareness and impossible worlds structures interpreted on neighborhood semantics and prove the two systems to be equally expressive.

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26

Shaffer, Michael J. "Safety, the Preface Paradox and Possible Worlds Semantics." Axiomathes 29, no. 4 (November 22, 2018): 347–61. http://dx.doi.org/10.1007/s10516-018-9413-3.

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27

Benson, Christine, and Mark Sand. "CONCEPTS VERSUS FACTS: THE BEST OF BOTH WORLDS." PRIMUS 9, no. 4 (January 1999): 365–73. http://dx.doi.org/10.1080/10511979908965942.

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28

Cruz Vázquez, Jonathan Axel, Elena Fabiola Ruiz Ledesma, and Lorena Chavarría Báez. "Virtual worlds in distance learning." International Journal of Evaluation and Research in Education (IJERE) 11, no. 2 (June 1, 2022): 907. http://dx.doi.org/10.11591/ijere.v11i2.21752.

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<span lang="EN-US">Virtual worlds are considered an additional proposal within the e-learning model. Online platforms have not been enough resources to be successful in the teaching and learning processes, therefore, it is necessary to search more options that contribute to their improvement. Virtual worlds, through inverse and visual experiences for the student, offer new panoramas that allow living situations and solving problems in different areas, such as mathematics. This article analyzes the opinion of higher-level students regarding the use of virtual worlds in their distance classes. Likewise, the virtual worlds provide help in improving teacher-student and student-student relationships. Some cases of educational institutions that integrated the use of virtual worlds into their classes are shown. A Likert-type scale questionnaire has been applied to a sample of 65 higher-level students. Its reliability was validated by means of Cronbach's alpha coefficients and Pearson's. It was found that students consider that the use of virtual worlds would improve class work and relationships between their peers and their teachers. It is remarkably undoubted that virtual worlds within education path are considered an excellent tool for e-learning. However, although the interest on the part of students is high, it is necessary to carry out more researching and developing procedures on the virtual worlds as an alternative to support learning. </span>

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29

Hannula, Jani. "Matematiikan kuusi osaa: David Tallin matematiikan kolmen maailman viitekehyksen laajentaminen Juha Oikkosen matematiikan kaksilla kasvoilla." Lumat: International Journal of Math, Science and Technology Education 2, no. 1 (January 30, 2014): 59–68. http://dx.doi.org/10.31129/lumat.v2i1.1082.

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The three worlds of mathematics by David Tall provide a framework for studying mathematical thinking and its development. Extending the framework of three worlds by Tall with Juha Oikkonen’s ”two faces of mathematics” develops a new, broader framework in which certain aspects to research on learning mathematics (such as mini-theories) are included to form a larger entity. The framework, previously drafted by Oikkonen and more thoroughly analyzed in this article, has the power to explain, for example, the learning processes of individual mathematical concepts.

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30

Fraigniaud, Pierre, Cyril Gavoille, and Christophe Paul. "Eclecticism shrinks even small worlds." Distributed Computing 18, no. 4 (February 3, 2006): 279–91. http://dx.doi.org/10.1007/s00446-005-0137-4.

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31

Grossman, Jerrold W., and Duncan J. Watts. "Small Worlds: The Dynamics of Networks between Order and Randomness." American Mathematical Monthly 107, no. 7 (August 2000): 664. http://dx.doi.org/10.2307/2589138.

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32

Shrestha, Mahesh M. "Dimensions of Creation of the Universe and the Living Worlds." European Journal of Theology and Philosophy 1, no. 4 (August 8, 2021): 1–8. http://dx.doi.org/10.24018/theology.2021.1.4.34.

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The Cosmos we live in consists of Invisible Prakriti and Visible World. In Visible World, we do live. All the galaxies, Milky Ways, nebulas and planets, stars, and physical bodies belong to this world are governed by the physical and mathematical laws of nature. Prakriti which is invisible spiritually governed and wave-formed existed even before the Big-Bang. Purush holds the Visible World and Prakriti around makes entire Cosmos in existence. Purush which is an absolutely positively charged and quality less with no traces of negative portions always existed, neither being created nor destroyed. A fraction of a Purush known as Omega Point appears into the portion of Prakriti due to some causal effect for further expansion of the Visible World. Purush is situated in the middle of the cylindrical universe surrounded by the Prakriti and Visible World. Theories proposed by different scientists and philosophers to verify the Purush seem to be incomplete trial and error of the zigzag puzzle show. Today, our scientists, cosmologists, and mathematicians are trying to explain the function of the universe through only four physical dimensions of science, which seems to be incomplete without explaining the transcendental factors while dealing with the living bodies.

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33

Sheynin, Oscar. "Ivar Ekeland, The best of all possible worlds. Mathematics and destiny." Almagest 2, no. 2 (January 2011): 146–47. http://dx.doi.org/10.1484/j.alma.4.1009.

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34

Smith, Gregory J., John S. Gero, and Mary Lou Maher. "Towards Designing in Adaptive Virtual Worlds." Computer-Aided Design and Applications 1, no. 1-4 (January 2004): 701–8. http://dx.doi.org/10.1080/16864360.2004.10738316.

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35

CHAUDHURI, KAUSTUV, JOËLLE DESPEYROUX, CARLOS OLARTE, and ELAINE PIMENTEL. "Hybrid linear logic, revisited." Mathematical Structures in Computer Science 29, no. 8 (April 22, 2019): 1151–76. http://dx.doi.org/10.1017/s0960129518000439.

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HyLL (Hybrid Linear Logic) is an extension of intuitionistic linear logic (ILL) that has been used as a framework for specifying systems that exhibit certain modalities. In HyLL, truth judgements are labelled by worlds (having a monoidal structure) and hybrid connectives (at and ↓) relate worlds with formulas. We start this work by showing that HyLL's axioms and rules can be adequately encoded in linear logic (LL), so that one focused step in LL will correspond to a step of derivation in HyLL. This shows that any proof in HyLL can be exactly mimicked by a LL focused derivation. Another extension of LL that has extensively been used for specifying systems with modalities is Subexponential Linear Logic (SELL). In SELL, the LL exponentials (!, ?) are decorated with labels representing locations, and a pre-order on such labels defines the provability relation. We propose an encoding of HyLL into SELL⋒ (SELL plus quantification over locations) that gives better insights about the meaning of worlds in HyLL. More precisely, we identify worlds as locations, and show that a flat subexponential structure is sufficient for representing any world structure in HyLL. This shows that HyLL's monoidal structure is not reflected in LL derivations, hence not increasing the expressiveness of LL, from a proof theoretical point of view. We conclude by proposing the notion of fixed points in multiplicative additive HyLL (μHyMALL), which can be encoded into multiplicative additive linear logic with fixed points (μMALL). As an application, we propose encodings of Computational Tree Logic (CTL) into both μMALL and μHyMALL. In the former, states are represented as atoms in the linear context, hence reflecting a more operational view of CTL connectives. In the latter, worlds represent states of the transition system, thus exhibiting a pleasant similarity with the semantics of CTL.

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36

Cyranek, Günther. "Social implications of virtual worlds." Digital Creativity 13, no. 1 (March 2002): 1–2. http://dx.doi.org/10.1076/digc.13.1.1.3215.

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37

Kauffman, Louis H. "Calculus, Gauge Theory and Noncommutative Worlds." Symmetry 14, no. 3 (February 22, 2022): 430. http://dx.doi.org/10.3390/sym14030430.

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This paper shows how gauge theoretic structures arise in a noncommutative calculus where the derivations are generated by commutators. These patterns include Hamilton’s equations, the structure of the Levi–Civita connection, and generalizations of electromagnetism that are related to gauge theory and with the early work of Hermann Weyl. The territory here explored is self-contained mathematically. It is elementary, algebraic, and subject to possible generalizations that are discussed in the body of the paper.

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38

Tang, Yanfeng, Chenchen Wei, Shoulong Cheng, and Zhi Huang. "Stereo visual-inertial odometry using structural lines for localizing indoor wheeled robots." Measurement Science and Technology 33, no. 5 (February 18, 2022): 055114. http://dx.doi.org/10.1088/1361-6501/ac46ef.

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Abstract This paper proposes optimization-based stereo visual-inertial odometry (VIO) to locate indoor wheeled robots. The multiple Manhattan worlds (MWs) assumption is adopted to model the interior environment. Instead of treating these worlds as isolated ones, we fuse the latest MW with the previous ones if they are in the same direction, reducing the calculated errors on the orientation of the latest MW. Then, the structural lines that encode the orientation information of these worlds are taken as additional landmarks to improve the positioning accuracy and reduce the accumulated drift of the system, especially when the system is in a challenging environment (i.e. scenes with continuous turning and low textures). In addition, the structural lines are parameterized by only two variables, which improves the computational efficiency and simplifies the initialization of lines. Experiments on public benchmark datasets and in real-world environments demonstrate that the proposed VIO system can accurately position the wheeled robot in a complex indoor environment.

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39

Ognjanovic, Zoran, and Nebojsa Ikodinovic. "A logic with higher order conditional probabilities." Publications de l'Institut Math?matique (Belgrade), no. 96 (2007): 141–54. http://dx.doi.org/10.2298/pim0796141o.

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We investigate probability logic with the conditional probability operators This logic, denoted LCP, allows making statements such as: P?s?, CP?s(? | ?) CP?0(? | ?) with the intended meaning "the probability of ? is at least s" "the conditional probability of ? given ? is at least s", "the conditional probability of ? given ? at most 0". A possible-world approach is proposed to give semantics to such formulas. Every world of a given set of worlds is equipped with a probability space and conditional probability is derived in the usual way: P(? | ?) = P(?^?)/P(?), P(?) > 0, by the (unconditional) probability measure that is defined on an algebra of subsets of possible worlds. Infinitary axiomatic system for our logic which is sound and complete with respect to the mentioned class of models is given. Decidability of the presented logic is proved.

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40

Cockell, Charles S. "Habitable worlds with no signs of life." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 372, no. 2014 (April 28, 2014): 20130082. http://dx.doi.org/10.1098/rsta.2013.0082.

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‘Most habitable worlds in the cosmos will have no remotely detectable signs of life’ is proposed as a biological hypothesis to be tested in the study of exoplanets. Habitable planets could be discovered elsewhere in the Universe, yet there are many hypothetical scenarios whereby the search for life on them could yield negative results. Scenarios for habitable worlds with no remotely detectable signatures of life include: planets that are habitable, but have no biosphere (Uninhabited Habitable Worlds); planets with life, but lacking any detectable surface signatures of that life (laboratory examples are provided); and planets with life, where the concentrations of atmospheric gases produced or removed by biota are impossible to disentangle from abiotic processes because of the lack of detailed knowledge of planetary conditions (the ‘problem of exoplanet thermodynamic uncertainty’). A rejection of the hypothesis would require that the origin of life usually occurs on habitable planets, that spectrally detectable pigments and/or metabolisms that produce unequivocal biosignature gases (e.g. oxygenic photosynthesis) usually evolve and that the organisms that harbour them usually achieve a sufficient biomass to produce biosignatures detectable to alien astronomers.

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41

Horn, Daniel, Ewen Cheslack-Postava, Tahir Azim, Michael J. Freedman, and Philip Levis. "Scaling Virtual Worlds with a Physical Metaphor." IEEE Pervasive Computing 8, no. 3 (July 2009): 50–54. http://dx.doi.org/10.1109/mprv.2009.54.

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42

WELCH, JOHN W. "WEIGHING & MEASURING IN THE WORLDS OF THE BOOK OF MORMON." Journal of Book of Mormon Studies (1992-2007) 8, no. 2 (October 1, 1999): 36–86. http://dx.doi.org/10.2307/44747520.

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43

Krysztofiak, Wojciech. "The phenonenological idealism controversy in light of possible worlds semantics." Axiomathes 17, no. 1 (February 14, 2007): 75–97. http://dx.doi.org/10.1007/s10516-006-9005-5.

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44

Besnard, Philippe, and Torsten Schaub. "POSSIBLE WORLDS SEMANTICS FOR DEFAULT LOGICS." Fundamenta Informaticae 21, no. 1,2 (1994): 39–66. http://dx.doi.org/10.3233/fi-1994-21123.

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45

Dukes, Mark, Einan Gardi, Einar Steingrímsson, and Chris D. White. "Web worlds, web-colouring matrices, and web-mixing matrices." Journal of Combinatorial Theory, Series A 120, no. 5 (July 2013): 1012–37. http://dx.doi.org/10.1016/j.jcta.2013.02.001.

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46

Marr (book editor), Alexander, and Bernardo Mota (review author). "The Worlds of Oronce Fine: Mathematics, Instruments and Print in Renaissance France." Aestimatio: Critical Reviews in the History of Science 8 (December 21, 2015): 30–33. http://dx.doi.org/10.33137/aestimatio.v8i0.25941.

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47

Oosterhoff, Richard J. "The Worlds of Oronce Fine. Mathematics, Instruments and Print in Renaissance France." Intellectual History Review 20, no. 4 (December 2010): 525–27. http://dx.doi.org/10.1080/17496977.2010.525921.

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48

Gauvin, J. F. "The Worlds of Oronce Fine: Mathematics, Instruments and Print in Renaissance France." French History 26, no. 4 (September 17, 2012): 545–47. http://dx.doi.org/10.1093/fh/crs095.

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49

Davis, Chandler. "The Best of All Possible Worlds: Mathematics and Destiny (review)." University of Toronto Quarterly 78, no. 1 (2009): 143–44. http://dx.doi.org/10.1353/utq.0.0394.

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50

Bernardoni, Andrea. "The Worlds of Oronce Fine: Mathematics, Instruments and Print in Renaissance France." Nuncius 26, no. 2 (2011): 409–10. http://dx.doi.org/10.1163/182539111x569919.

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