Observations of apparently random phenomena are commonplace in science. However, randomness and Christian belief are often seen as incompatible, both by naturalists and by theists. This article argues that the scientific concept of randomness and the historic Christian understanding of God’s nature are compatible. It argues that the existence of randomness cannot be settled scientifically; neve...

This document presents the results of the seminar “Conceptual Architecture Patterns” of the winter term 2002 in the Hasso–Plattner–Institute. It is a compilation of the student’s elaborations dealing with some conceptual architecture patterns which can be found in literature. One important focus laid on the runtime structures and the presentation of the patterns.

We argue that visual, analogical representations of mathematical concepts can be used by automated theory formation systems to develop further concepts and conjectures in mathematics. We consider the role of visual reasoning in human development of mathematics, and consider some aspects of the relationship between mathematics and the visual, including artists using mathematics as inspiration fo...

The gestures children spontaneously produce when explaining a task predict whether they will subsequently learn that task. Why? Gesture might simply reflect a child's readiness to learn a particular task. Alternatively, gesture might itself play a role in learning the task. To investigate these alternatives, we experimentally manipulated children's gesture during instruction in a new mathematic...

In the search for principles of pattern generation in complex biological systems, an operational approach is presented that embraces both theory and experiment. The central mathematical concepts of self-organization in nonequilibrium systems (including order parameter dynamics, stability, fluctuations, and time scales) are used to show how a large number of empirically observed features of temp...

Resumen Background: The goal of this study was to develop and validate the Family Motivational Climate Questionnaire (FMCQ). Parental involvement (PI) affects children’s academic orientations. However, PI questionnaires had not considered parenting behaviours from the perspective of motivational theories. It was therefore decided to develop the FMCQ. Method: 570 Secondary-School students formed...

The purpose of this study is to present evidence of how base-ten-blocks have been developed and emphasized as a tool for learning in mathematics education. After an introduction of the theme, we discuss the theoretical and epistemological perspectives that provide the basis for our analysis of the literature. Then, we illustrate how base-ten-blocks have historically been associated with the num...

In this paper we describe the use of fuzzy mathematical concepts in spotting characters from continuous speech in the Indian language Hindi. The research effort reported here is concerned with identifying the phonetic features from the acoustic parameters of a speech signal and combining the features to spot a character in continuous speech. These functions are performed by using expert systems...

We use the Michelson-Morley experiment as a case study in validation based on current knowledge. We use standard mathematical concepts of error analysis to develop measures of merit. In order to fully understand the case study, we review philosophical concepts, focusing on scientific confirmation. We review confirmation to understand formal logical concepts that can be used. We then propose a l...

1 Why Lie groups? As mathematicians, we are excited by the profundity and sthetic majesty of mathematical concepts. Yet, as numerical analysts, we cannot escape this elementary test: how much does a given construct, beautiful as it might be, help us to elucidate the nature of the computational phenomenon that we happen to investigate? Nothing can be taken for granted without justiication and, b...