Diagrammatic Reasoning and Modelling in the Imagination: The Secret Weapons of the Scientific Revolution

Just before the Scientific Revolution, there was a "Mathematical Revolution", heavily based on geometrical and machine diagrams. The "faculty of imagination" (now called scientific visualization) was developed to allow 3D understanding of planetary motion, human anatomy and the workings of machines. 1543 saw the publication of the heavily geometrical work of Copernicus and Vesalius, as well as the first Italian translation of Euclid

The hardness of the iconic must: Can Peirce’s existential graphs assist modal epistemology?

Charles Peirce’s diagrammatic logic - the Existential Graphs - is presented as a tool for illuminating how we know necessity, in answer to Benacerraf’s famous challenge that most “semantics for mathematics” do not “fit an acceptable epistemology”. It is suggested that necessary reasoning is in essence a recognition that a certain structure has the structure that it has. This means that, contra Hume and his contemporary heirs, necessity is observable. One just needs to pay attention, not just to individual things but to how those things are related in larger structures, certain aspects of which force certain others to be a particular way

Inducing visibility and visual deduction

Scientists use diagrams not just to visualize objects and relations in their fields, both empirical and theoretical, but to reason with them as tools of their science. While the two dimensional space of diagrams might seem restrictive, scientific diagrams can depict many more than two elements, can be used to visualise the same materials in myriad different ways, and can be constructed in a considerable variety of forms. This paper takes up two generic puzzles about 2D visualizations. First: How do scientists in different communities use 2D spaces to depict materials which are not fundamentally spatial? This prompts the distinction between diagrams that operate in different kinds of spaces: ‘real’, ‘ideal’, and ‘artificial’. And second: How do diagrams, in these different usages of 2D space, support various kinds of visual reasoning that cross over between inductive and deductive? The argument links the representational form and content of a diagram (its vocabulary and grammar) with the kinds of inferential and manipulative reasoning that are afforded, and constrained, by scientists’ different usages of 2D space

The Translocal Event and the Polyrhythmic Diagram

This thesis identifies and analyses the key creative protocols in translocal performance practice, and ends with suggestions for new forms of transversal live and mediated performance practice, informed by theory. It argues that ontologies of emergence in dynamic systems nourish contemporary practice in the digital arts. Feedback in self-organised, recursive systems and organisms elicit change, and change transforms. The arguments trace concepts from chaos and complexity theory to virtual multiplicity, relationality, intuition and individuation (in the work of Bergson, Deleuze, Guattari, Simondon, Massumi, and other process theorists). It then examines the intersection of methodologies in philosophy, science and art and the radical contingencies implicit in the technicity of real-time, collaborative composition. Simultaneous forces or tendencies such as perception/memory, content/ expression and instinct/intellect produce composites (experience, meaning, and intuition- respectively) that affect the sensation of interplay. The translocal event is itself a diagram - an interstice between the forces of the local and the global, between the tendencies of the individual and the collective. The translocal is a point of reference for exploring the distribution of affect, parameters of control and emergent aesthetics. Translocal interplay, enabled by digital technologies and network protocols, is ontogenetic and autopoietic; diagrammatic and synaesthetic; intuitive and transductive. KeyWorx is a software application developed for realtime, distributed, multimodal media processing. As a technological tool created by artists, KeyWorx supports this intuitive type of creative experience: a real-time, translocal “jamming” that transduces the lived experience of a “biogram,” a synaesthetic hinge-dimension. The emerging aesthetics are processual – intuitive, diagrammatic and transversal

Landau equations and asymptotic operation

The pinched/non-pinched classification of intersections of causal singularities of propagators in Minkowski space is reconsidered in the context of the theory of asymptotic operation as a first step towards extension of the latter to non-Euclidean asymptotic regimes. A highly visual distribution-theoretic technique of singular wave fronts is tailored to the needs of the theory of Feynman diagrams. Besides a simple derivation of the usual Landau equations in the case of the conventional singularities, the technique naturally extends to other types of singularities e.g. due to linear denominators in non-covariant gauges etc. As another application, the results of Euclidean asymptotic operation are extended to a class of quasi-Euclidean asymptotic regimes in Minkowski space.Comment: 15p PS (GSview), IJMP-A (accepted