Spatial Intuition Research Articles

The Structure of the Place and Its Transformations in TV Drama

The diversity of narrative methods has opened up new horizons in the process of recounting events and entering into narrative sequences, after which the dramatic text follows varying levels in the movement of dramatic events. This overlap in the narrative has made the artworker have multiple options in shaping his graphic structure, beginning with the formation of the logical introduction, the appearance of the actor, and leading to conflict and confrontation and the creation of tension and excitement. These methods, the multiple reading of the dramatic text, the formation of events, the building of a vision, the treatment, the development of excretive solutions and the creation of a virtual world, run in many strange and fantasi places, for those worlds, and the transformations of the dramatic event accompanied by a shift in space and time. Based on the movement of the operator, the search for its objective, the overlapping of the narrative systems, and its use in accordance with the narrative sequences created by the artworkmaker, the recipient is able to keep track of the events and expand the narrative of the events, as determined by the artwork industry, thus creating a beautiful response and arriving at the composition of the meaning of the visual output. Therefore, the problem of research can be formulated with the following question: What are the ways in which the dramatic narrative and spatial intuitions can be reflected in the output? The aim of the research is to detect dramatic robotics and spatial structure transformations in visual output.

Analisis Peningkatan Level Berpikir Geometri Mahasiswa Berdasarkan Teori Van Hiele dengan Pendekatan Konstruktivisme

The provision of problem-solving, analytical, systematic, critical, and creative skills is important to improve human resources that can be obtained from learning mathematics. Geometry is a field of mathematics that aims to develop logical thinking skills, develop spatial intuition, and interpret mathematical arguments. Several studies show that students' understanding of geometry material is still at a low level, so it is necessary to develop or improve the geometry learning process. The purpose of this study is to describe the increase in students' geometric thinking levels based on Van Hiele's theory with a constructivism approach. The method used in this research is descriptive qualitative with data analysis techniques using the Miles & Huberman model in the form of data reduction, data presentation, and drawing conclusions. The results showed that before the learning process using a constructivist approach, students' geometric thinking skills were at levels 1 to 3 or the analysis stage to a formal deduction with the average being at the informal deduction and pre-formal deduction stages. Meanwhile, after the learning process using a constructivist approach was carried out, geometric thinking skills increased at levels 2 to 4 or the informal deduction stage to the rigor with an average increase in the formal deduction stage.

Natural language modelled and printed in 3D: a multi-disciplinary approach

Natural language is a high-dimensional form that evolved through innovation and repetition over millennia. We tend to imagine language in the shape dictated by our writing system, as words on a page, or as sound. The aim of this paper is to explore how one aspect of this high-dimensional form could be rendered in 3D. Contemporary software developed for the production of film and video animation became a tool for us to model natural language. The paper begins with an overview of historical material about features of language and computational design that became relevant for our project. The whole system and structure of a language, its grammar has been compared to a geometry for centuries, as principles that define its shape. One aspect of this complex configuration was selected for 3D modelling; evidentiality. This aspect of every language points at the evidence for what people are saying. The paper lays out the research trajectory that allowed us to conceive of evidentiality as a third dimension, which is often lost in translation. We offer a step-by-step account of our methodology and 3D design process. Our findings consist of four introductory prototypes and digital 3D images, each one designed on the basis of a short language sample. The portrayal of a language excerpt as a digitally frozen shape enabled us to print natural language in 3D. Such 3D language objects not only extend the legacy of form-finding within computational design, but also allows for spatial intuition to help us get a more solid grasp of languages we may not speak.

Preliminary Results of Virtual Reality Mapping of E+A Galaxies and Candidates in Nearby Rich Clusters of Galaxies

Abstract In the study of large astronomical data sets, virtual reality (VR) can help build valuable spatial intuition for scientific discovery. We created VR visualizations of E+A galaxies and candidates in four nearby clusters of galaxies: Leo, Virgo, Hercules, and Coma. E+A's are a type of post-starburst galaxy in which all star formation has been recently (∼1 Gyr ago) quenched. Our E+A samples were assembled and cataloged by the Y/Dim collaboration through visual and quantitative analysis of SDSS DR16 spectra. The visualizations are designed for Oculus VR headsets, and utilize C# scripts which interface with the Unity engine, including public domain code and code developed by the lead author. We use these visualizations to find features of the aforementioned galaxy clusters: for instance, a “nose” of low velocity objects in the center of the Virgo cluster and a collection of E+A candidates along a galactic filament in the Coma cluster.

Der må være en kant. En diskussion af forskellige opfattelser af rum og virkelighed i lyset af Kants teori om rummet

This article discusses to what extent is makes sense to talk about different conceptions of space, and different experiences of space. According to Kant our sense perceptions are organized by a unique set of categories and by the form of our inner and outer sense, time and space respectively. To Kant, this spatial intuition is culturally invariant because it is a condition for the possibility of any experience whatsoever. Without accepting Kant’s terminology the author agrees that certain rudimentary abilities of spatial orientation have to be presupposed as universally shared. However, we do seem to have different ways of conceiving and thinking about space. Within our own culture we can distinguish between subjective/personal, public/official and scientific conceptions of space. It is argued that in other cultures, where these conceptions are different, we should be weary of a quasi-Kantian position which attributes such differences to differences in ‘categorial schemes’, and which further claims that these are conditions for the possibility of experience in this specific culture. Such a culturally speciftc a priori category confuses conditions for any possible experience with possible experiences. Furthermore, it ignores epistemological distinctions we readily employ within our own cultures.

Transformed Shell Roof Structures as the Main Determinant in Creative Shaping Building Free Forms Sensitive to Man-Made and Natural Environments

The article presents author’s propositions for shaping free forms of buildings sensitive to harmonious incorporation into built or natural environments. Complex folded structures of buildings roofed with regular shell structures are regarded as the most useful in creative shaping the free forms that can easily adapt to various expected environmental conditions. Three more and more sophisticated methods are proposed for creating variously conditioned free form structures. The first method allows the possibility of combining many single free forms into one structure and leaves the designer full freedom in shaping regular or irregular structures. The second, more sophisticated method introduces additional rules supporting the designer's spatial reasoning and intuition in imposing regularity of the shapes of the building structure and its roof shell structure. The third, most sophisticated method introduces additional conditions allowing the optimization of the regular shapes and arrangement of complete shell roof segments on the basis of an arbitrary reference surface and a finite number of straight lines normal to the surface. This original, interdisciplinary study offers new insight into, and knowledge of, unconventional methods for the creative shaping of innovative free forms, where great possibility and significant restrictions result from geometrical and mechanical properties of the materials used. Solving a number of issues in the field of civil engineering, descriptive geometry and architecture is crucial in the process of creating these structures.

Intuitive Mathematical Economics Series. Linear Structures I. Linear Manifolds, Vector Spaces and Scalar Products

Linear algebra is undoubtedly one of the most powerful structures of pure and applied mathematics. It combines extreme generality with deeply held spatial intuitions. In economics and data science, one would dare to say, lies at the basis of most of the other mathematical techniques used. Yet, standard presentations of the subject tend to refrain from displaying the full extent of the deeply intuitive nature of the underlying structures, despite the fact that such intuitions are so useful when applying linear algebra, and when extending techniques to tackle nonlinear problems. In the context of the “Intuitive Mathematical Economics Series”, this is the first paper of a series dedicated to presenting linear algebra emphasizing both, its intuitive, and its general nature. In this case we present linear manifolds and vector spaces.

Promoting preschoolers' numerical knowledge through spatial analogies: Numbers’ spatial alignment influences its learning

The development of early numerical representations is a complex cognitive process whereby children acquire numerical competences. To establish whether analogy making plays a role in this process of learning, we devised a classroom game based on an analysis of a number-line analogy that leverages children' spatial intuitions for helping them understand the numbers. To investigate the role of spatial positioning along the number line, seventy-seven preschoolers were randomly assigned to control tasks (control condition) or to embodied number line tasks in two possible spatial locations: watching numbers increasing either from left to right (space-number alignment condition) or from right to left (space-number misalignment condition). Performing learning activities for roughly two hours promoted children's proficiency in four tasks of numerical knowledge, but only children under spatial and numerical alignment increased their proficiency in a task of number line estimation. This finding shows that the numerical representations generated by children during training were integrated with spatial information that was implicit in the learning activities, thus revealing that analogical alignments play a key role in the formation of early numerical representations. Additionally, this study illustrates that interrogating the analogy at the foundation of an instructional activity highlights key instructional decisions that can have a large impact on learning. Future research along this line might provide a framework for using analogy at the foundations of instructional design.

Editorial: The role of reasoning in mathematical thinking

ABSTRACTResearch into mathematics often focuses on basic numerical and spatial intuitions, and one key property of numbers: their magnitude. The fact that mathematics is a system of complex relationships that invokes reasoning usually receives less attention. The purpose of this special issue is to highlight the intricate connections between reasoning and mathematics, and to use insights from the reasoning literature to obtain a more complete understanding of the processes that underlie mathematical cognition. The topics that are discussed range from the basic heuristics and biases to the various ways in which complex, effortful reasoning contributes to mathematical cognition, while also considering the role of individual differences in mathematics performance. These investigations are not only important at a theoretical level, but they also have broad and important practical implications, including the possibility to improve classroom practices and educational outcomes, to facilitate people's decision-making, as well as the clear and accessible communication of numerical information.

After Non-Euclidean Geometry: Intuition, Truth and the Autonomy of Mathematics

The mathematical developments of the 19th century seemed to undermine Kant’s philosophy. Non-Euclidean geometries challenged Kant’s view that there is a spatial intuition rich enough to yield the truth of Euclidean geometry. Similarly, advancements in algebra challenged the view that temporal intuition provides a foundation for both it and arithmetic. Mathematics seemed increasingly detached from experience as well as its form; moreover, with advances in symbolic logic, mathematical inference also seemed independent of intuition. This paper considers various philosophical responses to these changes, focusing on the idea of modifying Kant’s conception of intuition in order to accommodate the increasing abstractness of mathematics. It is argued that far from clinging to an outdated paradigm, programs based on new conceptions of intuition should be seen as motivated by important philosophical desiderata, such as the truth, apriority, distinctiveness and autonomy of mathematics.

The Region Unknotting Game

SummaryMotivated by rcent work by A. Shimizu on a newly discovered unknotting operation and inspired by previous work on knot games, we introduce the Region Unknotting Game. We play the game on several types of knot diagrams, developing both our spatial intuition and our understanding of the structure of knots.

Frege’s philosophy of geometry

In this paper, I critically discuss Frege’s philosophy of geometry with special emphasis on his position in The Foundations of Arithmetic of 1884. In Sect. 2, I argue that that what Frege calls facultyof intuition in his dissertation (1873) is probably meant to refer to a capacity of visualizing geometrical configurations structurally in a way which is essentially the same for most Western educated human beings. I further suggest that according to his Habilitationsschrift (1874) it is through spatial intuition that we come to know the axioms of Euclidean geometry. In Sect. 3, I argue that Frege seems right in claiming in The Foundations, §14 that the synthetic nature of the Euclidean axioms follows from the fact that they are independent of one another and of the primitive laws of logic. If the former were dependent on (provable from) the latter, they would be analytic in Frege’s sense of analyticity. But then they would not be independent of one another and due to their mutual provability would lose their status as axioms of Euclidean geometry, since according to Frege an axiom of a theory T is per definitionen unprovable in T. I further argue that only by invoking pure spatial intuition can Frege “explain” the (alleged) epistemological status of the axioms of Euclidean geometry completely: their synthetic a priori nature. Finally, I argue that his view about independence in The Foundations, §14 seems to clash with his conception of independence in his mature period. In Sect. 4, I scrutinize Frege’s somewhat vague, but unduly neglected remarks in The Foundations, §26 on space, spatial intuition and the axioms of Euclidean geometry. I argue that for the sake of coherence Frege should have said unambiguously that space is objective, that it is independedent not only of our spatial intuition, but of our mental life altogether including our judgements about space, instead of encouraging the possible conjecture that in his view it contains an objective and a subjective component. I further argue that for Frege the objectivity of both space and the axioms of Euclidean geometry manifests itself in our universal and compulsory acknowledgement of the Euclidean axioms as true. I conclude Sect. 4 by arguing that there is a conflict between the subjectivity of our spatial intuitions as stressed in The Foundations, §26 and Frege’s thesis in his dissertation that the axioms of Euclidean geometry derive their validity from the nature of our faculty of intuition. To resolve this conflict, I propose that in the light of his avowed realism in The Foundations Frege could have replaced his early thesis by saying that although we come to know the axioms of Euclidean geometry through spatial intuition and are justified in acknowledging them as true on the basis of geometrical intuition, their truth is independent not only of the nature of our faculty of intuition and singular acts of intuition, but of our mental processes and activities in general, including the inner mental act of judging. In Sect. 5, I argue that Frege most likely did not adopt Kant’s method of acquiring geometrical knowledge via the ostensive construction of concepts in spatial intuition. In contrast to Kant, Frege holds that the axioms of three-dimensional Euclidean geometry express state of affairs about space obtaining independently of our spatial intuition. In Sect. 6, I conclude with a summarized assessment of Frege’s philosophy of geometry.

Hippocampal spatial mechanisms relate to the development of arithmetic symbol processing in children

Understanding the meaning of abstract mathematical symbols is a cornerstone of arithmetic learning in children. Studies have long focused on the role of spatial intuitions in the processing of numerals. However, it has been argued that such intuitions may also underlie symbols that convey fundamental arithmetic concepts, such as arithmetic operators. In the present cross-sectional study, we used fMRI to investigate how and when associations between arithmetic operators and brain regions processing spatial information emerge in children from 3rd to 10th grade. We found that the mere perception of a ‘+’ sign elicited grade-related increases of spatial activity in the right hippocampus. That is, merely perceiving ‘+’ signs – without any operands – elicited enhanced hippocampal activity after around 7th grade (12–13 years old). In these children, hippocampal activity in response to a ‘+’ sign was further correlated with the degree to which calculation performance was facilitated by the preview of that sign before an addition problem, an effect termed operator-priming. Grade-related increases of hippocampal spatial activity were operation-specific because they were not observed with ‘×’ signs, which might evoke rote retrieval rather than numerical manipulation. Our study raises the possibility that hippocampal spatial mechanisms help build associations between some arithmetic operators and space throughout age and/or education.

What's Behind a “+” Sign? Perceiving an Arithmetic Operator Recruits Brain Circuits for Spatial Orienting

Do mathematical symbols evoke spatial representations? Although behavioral studies have long demonstrated interactions between space and the processing of Arabic digits, how to interpret these results remains controversial. Here, we tested whether activity in regions supporting spatial processing contributes to the processing of symbols conveying fundamental arithmetic concepts-such as operation signs-even in the absence of associated digits. Using functional magnetic resonance imaging, we show that merely perceiving a "+" sign triggers activity in brain regions that support the orienting of spatial attention in adults. Activity in these regions was greater for "+" than for "×" signs, indicating that it is modulated by whether an operator reflects an operation that evokes numerical manipulation (rather than rote memorization). Finally, the degree to which subjects activated a spatial region in response to a "+" sign was correlated with the degree to which subjects benefited from being briefly presented with that sign before having to calculate a single-digit addition problem, an effect termed operator-priming. Therefore, not only are some arithmetic operators linked to spatial intuitions, but such intuitions might also have an important role during arithmetic calculation. More generally, our findings support the view that mathematical symbols inherently evoke spatial representations.

On the “negative utility” of Ernst Cassirer׳s philosophy of physics: An application to the EPR argument

This paper tries to reconstruct Ernst Cassirer's potential reception of the EPR argument, as exposed by Einstein in his letter to Cassirer of March 1937. It is shown that, in conformity with his transcendental epistemology taking the conditions of accessibility as constitutive of the quantum object, Cassirer would probably have rejected the argument. Indeed, Cassirer would probably not have subscribed to its separability/local causality presupposition (which goes against his interpretation of the quantum formalism as a self-sufficient condition constitutive of the quantum object, without any reliance on spatial intuition), nor to its completeness requirement (as his partial endorsement of Bohr's complementarity, and his rejection of the Kantian "idea of complete determination", illustrate). By rejecting both of its premises, Cassirer's philosophy of physics thus enables to escape the EPR dilemma, and exhibits what, in Kantian terms, might be called a "negative utility" with respect to physical science. A further investigation of the anti-reductionist utility of Cassirer's systematic philosophy with respect to physics and other "symbolic forms" is finally suggested.

Is There Any Room for Spatial Intuition in Riemann’s Philosophy of Geometry?

In his famous Habilitationsvortrag Riemann underlines important points on the very nature of space with respect to philosophy, mathematics, and physics. Although Riemann’s greatness in mathematics has been well acknowledged, and the importance and implications of his geometry studied widely by philosophers, the same does not seem to be true of his philosophy of geometry. In part, this paper is motivated by this very fact. In his Habilitationsvortrag Riemann sets aside the usual approaches that had been taken until then, and instead tries out new ideas and approaches. Riemann thought that while Euclidean geometry made an interesting proposal for the construction of a theory of space, there was in fact no a priori connection between the concept of space and the axioms of Euclidean geometry. He argued, then, that the fundamental concepts central to Euclidean geometry do not have to be part of every system of geometry imaginable. That is, the fundamental concepts of Euclidean geometry should not be thought of as necessary for the construction of all possible systems of geometry. Riemann wanted to depict nature from the perspective of its inner structures and one aspect of this endeavor entailed questioning the nature of space and geometry from heterogeneous points.

From Helmholtz to Schlick: The evolution of the sign-theory of perception

Efforts to trace the influence of fin de siècle neo-Kantianism on early 20th Century philosophy of science have led scholars to recognize the powerful influence on Moritz Schlick of Hermann von Helmholtz, the doyen of 19th Century physics and a leader of the zurȕck zu Kant movement. But Michael Friedman thinks that Schlick misunderstood Helmholtz' signature philosophical doctrine, the sign-theory of perception. Indeed, Friedman has argued that Schlick transformed Helmholtz' Kantian view of spatial intuition into an empiricist version of the causal theory of perception. However, it will be argued that, despite the key role the sign-theory played in his epistemology, Schlick thought the Kantianism in Helmholtz' thought was deeply flawed, rendered obsolete by philosophical insights which emerged from recent scientific developments. So even though Schlick embraced the sign-theory, he rejected Helmholtz' ideas about spatial intuition. In fact, like his teacher, Max Planck, Schlick generalized the sign-theory into a form of structural realism. At the same time, Schlick borrowed the method of concept-formation developed by the formalist mathematicians, Moritz Pasch and David Hilbert, and combined it with the conventionalism of Henri Poincaré. Then, to link formally defined concepts with experience, Schlick's introduced his ‘method of coincidences’, similar to the ‘point-coincidences’ featured in Einstein's physics. The result was an original scientific philosophy, which owed much to contemporary scientific thinkers, but little to Kant or Kantianism.

Chemical Bonds Visualization using Particle Effect and Augmented Reality

Augmented Reality (AR) is a research area that allow to overlay multimedia contents such as text and visual information onto real world through camera views. AR can be used to as an educational assistance to help student acquire a deep conceptual understanding and spatial intuition. The course material can be enriched by viewing multimedia content, as well as in tabletop AR environment. We present this paper an AR system for teaching chemical problem solving especialy chemical bonds to highschool students. Our system is built based on inexpensive webcams and open-source library. Chemical bonds are visualize through marker. By combine different markers, student can get different result and visualization. A survey was conducted after experience the AR chemical bonds, show great acceptance of system and visualization.

Putting spatial statistics (back) on the map

The literature in Geographical Information Science and Statistical Science often contains calls for analysts to “think spatially” and to “think statistically”, respectively, in order to gain better insight into proposed hypotheses. A central element of these calls involves the development of a spatial intuition or a statistical intuition, i.e., conceptual ways of framing questions, incorporating available data, calculating quantitative summaries, interpreting outcomes, and providing empirical answers from either a spatial or a statistical perspective. In this paper, I draw on past experience to identify and illustrate the potential for “spatial statistical thinking”, that is, the development of a spatial statistical intuition. Several examples illustrate the potential for a more explicit development of such intuition drawing simultaneously from both spatial analysis and statistics. As a step in this direction, I stress the importance of maintaining a spatial conceptual framework in the application and interpretation of spatial statistical methods, i.e., the importance of spatial interpretation of spatial statistics.

An Educational Resource for Spatial Intuition

The paper investigates the use of a 3D modular paper game within educational programs. The experiment involved students in grades 5 to 9, engaged in a guided play workshop, during a summer camp, in 2012, Romania. We report the conclusions on the use of this educational resource regarding its effectiveness in enhancing creativity and spatial intuition.