An investigation into the tension arising between natural language and mathematical language experienced by mechanical engineering students

This investigation is grounded within the concept of embodied cognition where the mind is considered to be part of a biological system. A first year undergraduate Mechanical Engineering cohort of students was tasked with explaining the behaviour of three balls of different masses being rolled down a ramp. The explanations given by the students highlighted the cognitive conflict between the everyday interpretation of the word energy and its mathematical use. The results showed that even after many years of schooling, students found it challenging to interpret the mathematics they had learned and relied upon pseudo-scientific notions to account for the behaviour of the balls.

Justice and morality:human suffering, natural law and international politics

Bridging the contending theories of natural law and international relations, this book proposes a 'relational ontology' as the basis for rethinking our approach to international politics. The book contains a number of challenging and controversial ideas on the study of international political thought which should provoke constructive debate within international relations theory, political theory, and philosophical ethics. © Amanda Russell Beattie 2010. All rights reserved.

Thomas, Howard, O'Neal, Don and Ghertman, Michael (Eds). Strategy, structure and style. Chichester: John Wiley, 1997

Book review

'Only in the leap from the lion's head will he prove his worth':natural law and international relations

This article argues the benefits of including a theological interpretation of natural law morality within the normative discourses of international politics. It challenges the assumption of a Grotian secular natural law arguing that practical reason, in a Thomist interpretation, is better suited to the demands of international political theory. It engages with themes of agency, practical reason, and community in order to enhance the content of the post-territorial community evidenced in ethical cosmopolitan debates. Likewise, it envisions a simultaneously enhancing a rapprochement among cosmopolitan and communitarian discourses of international politics facilitated through an institutional design guided by the morality of natural law.

Category structure affects the developmental trajectory of children’s inductive inferences for both natural kinds and artefacts

Inductive reasoning is fundamental to human cognition, yet it remains unclear how we develop this ability and what might influence our inductive choices. We created novel categories in which crucial factors such as domain and category structure were manipulated orthogonally. We trained 403 4-9-year-old children to categorise well-matched natural kind and artefact stimuli with either featural or relational category structure, followed by induction tasks. This wide age range allowed for the first full exploration of the developmental trajectory of inductive reasoning in both domains. We found a gradual transition from perceptual to categorical induction with age. This pattern was stable across domains, but interestingly, children showed a category bias one year later for relational categories. We hypothesise that the ability to use category information in inductive reasoning develops gradually, but is delayed when children need to process and apply more complex category structures. © 2014 © 2014 Taylor & Francis.

Transients and asymptotics of natural gradient learning

We analyse natural gradient learning in a two-layer feed-forward neural network using a statistical mechanics framework which is appropriate for large input dimension. We find significant improvement over standard gradient descent in both the transient and asymptotic phases of learning.

Response normalization and blur adaptation:data and multi-scale model

Adapting to blurred or sharpened images alters perceived blur of a focused image (M. A. Webster, M. A. Georgeson, & S. M. Webster, 2002). We asked whether blur adaptation results in (a) renormalization of perceived focus or (b) a repulsion aftereffect. Images were checkerboards or 2-D Gaussian noise, whose amplitude spectra had (log-log) slopes from -2 (strongly blurred) to 0 (strongly sharpened). Observers adjusted the spectral slope of a comparison image to match different test slopes after adaptation to blurred or sharpened images. Results did not show repulsion effects but were consistent with some renormalization. Test blur levels at and near a blurred or sharpened adaptation level were matched by more focused slopes (closer to 1/f) but with little or no change in appearance after adaptation to focused (1/f) images. A model of contrast adaptation and blur coding by multiple-scale spatial filters predicts these blur aftereffects and those of Webster et al. (2002). A key proposal is that observers are pre-adapted to natural spectra, and blurred or sharpened spectra induce changes in the state of adaptation. The model illustrates how norms might be encoded and recalibrated in the visual system even when they are represented only implicitly by the distribution of responses across multiple channels.