Gradually learning programming supported by a growable programming language

Learning programming is a difficult task. The learning process is particularly disorienting when you are approaching programming for the first time. As a student you are exposed to several new concepts (control flow, variable, etc. but also coding, compiling etc.) and new ways to think (algorithms). Teachers try to expose the students gradually to the new concepts by presenting them one by one but the tools at student's disposal do not help: they provide support, suggestion and documentation for the full programming language of choice hampering the teacher's efforts. On the other side, students need to learn real languages and not didactic languages. In this work we propose an approach to gradually teaching programming supported by a programming language that grows---together with its implementation---along with the number of concepts presented to the students. The proposed approach can be applied to the teaching of any programming language and some experiments with Javascript are reported

Symmetries and Special States in Two Dimensional String Theory

We use the W-infinity symmetry of c=1 quantum gravity to compute matrix model special state correlation functions. The results are compared, and found to agree, with expectations from the Liouville model.Comment: 20 page

Modelling recursion

The purpose of my research is to examine and explore the ways that undergraduate students understand the concept of recursion. In order to do this, I have designed computer-based software, which provides students with a virtual and interactive environment where they can explore the concept of recursion, and demonstrate and develop their knowledge of recursion through active engagement. I have designed this computer-based software environment with the aim of investigating how students think about recursion. My approach is to design digital tools to facilitate students' understanding of recursion and to expose that thinking. My research investigates students' understanding of the hidden layers and inherent complexity of recursion, including how they apply it within relevant contexts. The software design embedded the idea of functional abstraction around two basic principles of: 'functioning' and 'functionality'. The functionality principle focuses on what recursion achieve, and the functioning dimension concerns how recursion is operationalised. I wanted to answer the following crucial question: How does the recursive thinking of university students evolve through using carefully designed digital tools? In the process of exploring this main question, other questions emerged: 1. Do students understand the difference between recursion and iteration? 2. How is tail and embedded recursion understood by the students? 3. To what extent does prior knowledge of the concept of iteration influence students' understanding of tail and embedded recursion? 4. Why is it important to have a clear understanding of the control passing mechanisms in order to understand recursion? 5. What is the role of functional abstraction in both, the design of computer-based tools and the students' understanding of recursion? 6. How are students' mental models of recursion shaped by their engagement with computer-based tools? From a functional abstraction point of view almost all previous research into the concept of recursion has focused on the functionality dimension. Typically, it has focused on procedures for the calculation of the factorial of a natural number, and students were tested to see if they are able to work out the values of the a function recursively (Wiedenbeck, 1988; Anazi and Uesato, 1982) or if they are able to recognize a recursive structure (Sooriamurthi, 2001; Kurland and Pea, 1985). Also, I invented the Animative Visualisation in the Domain of Abstraction (AVDA) which combines the functioning and functionality principles regarding the concept of recursion. In the AVDA environment, students are given the opportunity to explore the hidden layers and the complicated behaviour of the control passing mechanisms of the concept of recursion. In addition, most of the textbooks in mathematics and computer sciences usually fail to explain how to use recursion to solve a problem. Although it is also true that text books do not typically explain how to use iteration to solve problems, students are able to draw on to facilitate solving iterative problems (Pirolli et al, 1988). My approach is inspired by how recursion can be found in everyday life and in real world phenomena, such as fractal-shaped objects like trees and spirals. This research strictly adheres to a Design Based Research methodology (DBR), which is founded on the principle of the cycle of designing, testing (observing the students' experiments with the design), analysing, and modifying (Barab and Squire, 2004; Cobb and diSessa, 2003). My study was implemented throughout three iterations. The results showed that in the AVDA (Animative Visualisation in the Domain of Abstraction) environment students' thinking about the concept of recursion changed significantly. In the AVDA environment they were able to see and experience the complicated control passing mechanism of the tail and embedded recursion, referred to a delegatory control passing. This complicated control passing mechanism is a kind of generalization of flow in the iterative procedures, which is discussed later in the thesis. My results show that, to model a spiral, students prefer to use iterative techniques, rather than tail recursion. The AVDA environment helped students to appreciate the delegatory control passing for tail recursive procedures. However, they still demonstrated difficulties in understanding embedded recursive procedures in modelling binary and ternary trees, particularly regarding the transition of flow between recursive calls. Based on the results of my research, I have devised a model of the evolution of students' mental model of recursion which I have called – the quasi-pyramid model. This model was derived from applying functional abstraction including both functionality and functioning principles. Pedagogic implications are discussed. For example, the teaching of recursion might adopt 'animative' visualization, which is of vitally important for students' understanding of latent layers of recursion

Normative Recursion : on Recursive Grounding and the Capacity for Radical Critique in Formal Pragmatics, Recognition, Social Freedom and Justification

This thesis explores the meta-ethical question: What properties would be required of a normative critical concept in order for it to be (a) derived from the social facticity of prevailing norms, practices and institutions in a given society and (b) still be capable of informing radical critique? This thesis takes radical critique to mean one that escapes all charges of status quo biases and thus truly transcends the immanent content of the norms, practices and institutions from which it was derived.This thesis asserts that the necessary property of such a concept is recursion. That is, the property of a self-referentiality that allows for something to hierarchically contain copies of itself. The idea of finding the property of recursion in normative political theory and defending its utility is undertheorized in the political theory literature. By locating the property of recursion in the formal pragmatics of Jürgen Habermas, in Axel Honneth’s concepts of recognition and social freedom and in Rainer Forst’s concept of justification, this thesis remedies this situation. In doing so, a space is carved out for normative political theory between foundationalism and anti-foundationalism and between the utopian and realist approach

The emergence of language as a function of brain-hemispheric feedback

This text posits the emergence of language as a function of brain-hemispheric feedback, where “emergence” refers to the generation of complex patterns from relatively simple interactions, “language” refers to an abstraction-based and representational-recombinatorial-recursive mapping-signaling system, “function” refers to an input-output relationship described by fractal algorithms, “brain-hemispheric” refers to complementary (approach-abstraction / avoidance-gestalt) cognitive modules, and “feedback” refers to self-regulation driven by neural inhibition and recruitment. The origin of language marks the dawn of human self-awareness and culture, and is thus a matter of fundamental and cross-disciplinary interest. This text is a synthesized research essay that constructs its argument by drawing diverse scholarly voices into a critical, cross-disciplinary intertextual narrative. While it does not report any original empirical findings, it harnesses those made by others to offer a tentative, partial solution—one that can later be altered and expanded—to a problem that has occupied thinkers for centuries. The research contained within this text is preceded by an introductory Section 1 that contextualizes the problem of the origin of language. Section 2 details the potential of evolutionary theory for addressing the problem, and the reasons for the century-long failure of linguistics to take advantage of that potential. Section 3 reviews the history of the discovery of brain lateralization, as well as its behavioral and structural characteristics. Section 4 discusses evolutionary evidence and mechanisms in terms of increasing adaptive complexity and intelligence, in general, and tool use, in particular. Section 5 combines chaos theory, brain science, and semiotics to propose that, after the neotenic acquisition of contingency-based abstraction, language emerged as a feedback interaction between the left-hemisphere abstract word and the right-hemisphere gestalt image. I conclude that the model proposed here might be a valuable tool for understanding, organizing, and relating data and ideas concerning human evolution, language, culture, and psychology. I recommend, of course, that I present this text to the scholarly community for criticism, and that I continue to gather and collate relevant data and ideas, in order to prepare its next iteration

Simulation of thermodynamic properties of magnetic transition metals from an efficient tight-binding model

Atomic scale simulations at finite temperature are an ideal approach to study the thermodynamic properties of magnetic transition metals. However, the development of interatomic potentials explicitly taking into account magnetic variables is a delicate task. In this context, we present a tight-binding model for magnetic transition metals in the Stoner approximation. This potential is integrated into a Monte Carlo structural relaxations code where trials of atomic displacements as well as fluctuations of local magnetic moments are performed to determine the thermodynamic equilibrium state of the considered systems. As an example, the Curie temperature of cobalt is investigated while showing the important role of atomic relaxations. Furthermore, our model is generalized to other transition metals highlighting a local magnetic moment distribution that varies with the gradual filling of the d states. Consequently, the successful validation of the potential for different magnetic configurations indicates its great transferability makes it a good choice for atomistic simulations sampling a large configuration space

Language: The missing selection pressure

Human beings are talkative. What advantage did their ancestors find in communicating so much? Numerous authors consider this advantage to be "obvious" and "enormous". If so, the problem of the evolutionary emergence of language amounts to explaining why none of the other primate species evolved anything even remotely similar to language. What I propose here is to reverse the picture. On closer examination, language resembles a losing strategy. Competing for providing other individuals with information, sometimes striving to be heard, makes apparently no sense within a Darwinian framework. At face value, language as we can observe it should never have existed or should have been counter-selected. In other words, the selection pressure that led to language is still missing. The solution I propose consists in regarding language as a social signaling device that developed in a context of generalized insecurity that is unique to our species. By talking, individuals advertise their alertness and their ability to get informed. This hypothesis is shown to be compatible with many characteristics of language that otherwise are left unexplained.Comment: 34 pages, 3 figure