Analysis of the Difficulty of Mathematical Education Students in Completing the Geometric Running Problem Based on Van Hiele Theory in Geometry Transformation

The purpose of this study was to: (1) finding out the difficulties experienced by mathematics education students in solving geometric reasoning problems based on van Hiele's theory; (2) identifying the factors causing difficulties experienced by students in solving geometric problems based on van Hiele’s theory; and (3) determining the steps that need to be taken to overcome the students' difficulties in solving geometric reasoning problems based on van Hiele's theory in the Transformation Geometry Course. The students' difficulties in solving geometric reasoning problems based on van Hiele's levels will give an idea of the indicators of geometrical reasoning abilities that are still low, so that the right alternative solutions are obtained. This type of research is descriptive research with a qualitative approach.  The research subjects were 28 students who programed geometry transformation courses. The instrument in this study was a test instrument, namely geometric reasoning abilities of students as many as 5 questions consisting of 5 levels of ability, namely visualization, analysis, abstraction, formal deduction, and rigor. While the data analysis techniques in this study used descriptive analysis. Collecting data in this study used interview techniques and written tests. The results showed that from the five indicators of geometric reasoning ability, for the visualization level, there were 26 people who achieved the optimal score with a percentage of 92.9. Seen at the level of analysis still not reached optimally with a percentage of 21.4 or only 6 people who achieved the optimal score, while the level of abstraction, formal deduction, and rigor has not been achieved. Difficulties experienced by students at the level of analysis, abstraction, formal deduction, and rigor. The causal factors experienced by students based on the results of interviews obtained information that students have difficulty answering questions due to several things including; students have forgotten about the material being taught, when they learn they understand but are less interested in developing, feel unsatisfied so they expect concrete media, need to be trained in many questions, and follow up to students. From this information, an appropriate alternative is needed, for example using van Hiele's theory to familiarize students with reasoning skills

On the Argument from Physics and General Relativity

I argue that the best interpretation of the general theory of relativity has need of a causal entity, and causal structure that is not reducible to light cone structure. I suggest that this causal interpretation of GTR helps defeat a key premise in one of the most popular arguments for causal reductionism, viz., the argument from physics

Geospatial Narratives and their Spatio-Temporal Dynamics: Commonsense Reasoning for High-level Analyses in Geographic Information Systems

The modelling, analysis, and visualisation of dynamic geospatial phenomena has been identified as a key developmental challenge for next-generation Geographic Information Systems (GIS). In this context, the envisaged paradigmatic extensions to contemporary foundational GIS technology raises fundamental questions concerning the ontological, formal representational, and (analytical) computational methods that would underlie their spatial information theoretic underpinnings. We present the conceptual overview and architecture for the development of high-level semantic and qualitative analytical capabilities for dynamic geospatial domains. Building on formal methods in the areas of commonsense reasoning, qualitative reasoning, spatial and temporal representation and reasoning, reasoning about actions and change, and computational models of narrative, we identify concrete theoretical and practical challenges that accrue in the context of formal reasoning about `space, events, actions, and change'. With this as a basis, and within the backdrop of an illustrated scenario involving the spatio-temporal dynamics of urban narratives, we address specific problems and solutions techniques chiefly involving `qualitative abstraction', `data integration and spatial consistency', and `practical geospatial abduction'. From a broad topical viewpoint, we propose that next-generation dynamic GIS technology demands a transdisciplinary scientific perspective that brings together Geography, Artificial Intelligence, and Cognitive Science. Keywords: artificial intelligence; cognitive systems; human-computer interaction; geographic information systems; spatio-temporal dynamics; computational models of narrative; geospatial analysis; geospatial modelling; ontology; qualitative spatial modelling and reasoning; spatial assistance systemsComment: ISPRS International Journal of Geo-Information (ISSN 2220-9964); Special Issue on: Geospatial Monitoring and Modelling of Environmental Change}. IJGI. Editor: Duccio Rocchini. (pre-print of article in press

Trapped surfaces and symmetries

We prove that strictly stationary spacetimes cannot contain closed trapped nor marginally trapped surfaces. The result is purely geometric and holds in arbitrary dimension. Other results concerning the interplay between (generalized) symmetries and trapped submanifolds are also presented.Comment: 9 pages, no figures. Final corrected version to appear in Class. Quantum Gra