Irrationality is needed to compute with signal machines with only three speeds

International audienceSpace-time diagrams of signal machines on finite configurations are composed of interconnected line segments in the Euclidean plane. As the system runs, a network emerges. If segments extend only in one or two directions, the dynamics is finite and simplistic. With four directions, it is known that fractal generation, accumulation and any Turing computation are possible. This communication deals with the three directions/sp eeds case. If there is no irrational ratio (between initial distances between signals or between speeds) then the network follows a mesh preventing accumulation and forcing a cyclic behavior. With an irrational ratio (here, the Golden ratio) between initial distances, it becomes possible to provoke an accumulation that generates infinitely many interacting signals in a bounded portion of the Euclidean plane. This b ehavior is then controlled and used in order to simulate a Turing machine and generate a 25-state 3-speed Turing-universal signal machin

Critical Market Crashes

This review is a partial synthesis of the book ``Why stock market crash'' (Princeton University Press, January 2003), which presents a general theory of financial crashes and of stock market instabilities that his co-workers and the author have developed over the past seven years. The study of the frequency distribution of drawdowns, or runs of successive losses shows that large financial crashes are ``outliers'': they form a class of their own as can be seen from their statistical signatures. If large financial crashes are ``outliers'', they are special and thus require a special explanation, a specific model, a theory of their own. In addition, their special properties may perhaps be used for their prediction. The main mechanisms leading to positive feedbacks, i.e., self-reinforcement, such as imitative behavior and herding between investors are reviewed with many references provided to the relevant literature outside the confine of Physics. Positive feedbacks provide the fuel for the development of speculative bubbles, preparing the instability for a major crash. We demonstrate several detailed mathematical models of speculative bubbles and crashes. The most important message is the discovery of robust and universal signatures of the approach to crashes. These precursory patterns have been documented for essentially all crashes on developed as well as emergent stock markets, on currency markets, on company stocks, and so on. The concept of an ``anti-bubble'' is also summarized, with two forward predictions on the Japanese stock market starting in 1999 and on the USA stock market still running. We conclude by presenting our view of the organization of financial markets.Comment: Latex 89 pages and 38 figures, in press in Physics Report

Proceedings of the ECCS 2005 satellite workshop: embracing complexity in design - Paris 17 November 2005

Embracing complexity in design is one of the critical issues and challenges of the 21st century. As the realization grows that design activities and artefacts display properties associated with complex adaptive systems, so grows the need to use complexity concepts and methods to understand these properties and inform the design of better artifacts. It is a great challenge because complexity science represents an epistemological and methodological swift that promises a holistic approach in the understanding and operational support of design. But design is also a major contributor in complexity research. Design science is concerned with problems that are fundamental in the sciences in general and complexity sciences in particular. For instance, design has been perceived and studied as a ubiquitous activity inherent in every human activity, as the art of generating hypotheses, as a type of experiment, or as a creative co-evolutionary process. Design science and its established approaches and practices can be a great source for advancement and innovation in complexity science. These proceedings are the result of a workshop organized as part of the activities of a UK government AHRB/EPSRC funded research cluster called Embracing Complexity in Design (www.complexityanddesign.net) and the European Conference in Complex Systems (complexsystems.lri.fr). Embracing complexity in design is one of the critical issues and challenges of the 21st century. As the realization grows that design activities and artefacts display properties associated with complex adaptive systems, so grows the need to use complexity concepts and methods to understand these properties and inform the design of better artifacts. It is a great challenge because complexity science represents an epistemological and methodological swift that promises a holistic approach in the understanding and operational support of design. But design is also a major contributor in complexity research. Design science is concerned with problems that are fundamental in the sciences in general and complexity sciences in particular. For instance, design has been perceived and studied as a ubiquitous activity inherent in every human activity, as the art of generating hypotheses, as a type of experiment, or as a creative co-evolutionary process. Design science and its established approaches and practices can be a great source for advancement and innovation in complexity science. These proceedings are the result of a workshop organized as part of the activities of a UK government AHRB/EPSRC funded research cluster called Embracing Complexity in Design (www.complexityanddesign.net) and the European Conference in Complex Systems (complexsystems.lri.fr)

On Folding: Towards a New Field of Interdisciplinary Research

It is only recently, with the increasing interest in origami and folding in natural sciences and the humanities, that the fold as a new conception in a whole range of disciplines has begun to be conceived in a broader way. Folding as a material and structural process offers a new methodology to think about the close relationship of matter, form and code. It henceforth crosses out old dichotomies, such as the organic and the inorganic or nature and technology, and blurs the boundaries between experimental, conceptual and historical approaches. This anthology aims to unfold this new interdisciplinary field and its disciplinary impact, ranging from materials science, biology, architecture, and mathematics to literature and philosophy

General Ecology: The New Ecological Paradigm

Ecology has become one of the most urgent and lively fields in both the humanities and sciences. In a dramatic widening of scope beyond its original concern with the coexistence of living organisms within a natural environment, it is now recognized that there are ecologies of mind, information, sensation, perception, power, participation, media, behavior, belonging, values, the social, the political… a thousand ecologies. This proliferation is not simply a metaphorical extension of the figurative potential of natural ecology: rather, it reflects the thoroughgoing imbrication of natural and technological elements in the constitution of the contemporary environments we inhabit, the rise of a cybernetic natural state, with its corresponding mode of power. Hence this ecology of ecologies initiates and demands that we go beyond the specificity of any particular ecology: a general thinking of ecology which may also constitute an ecological transformation of thought itself is required. In this ambitious and radical new volume of writings, some of the most exciting contemporary thinkers in the field take on the task of revealing and theorizing the extent of the ecologization of existence as the effect of our contemporary sociotechnological condition: together, they bring out the complexity and urgency of the challenge of ecological thought-one we cannot avoid if we want to ask and indeed have a chance of affecting what forms of life, agency, modes of existence, human or otherwise, will participate-and how-in this planet's future. - See more at: http://www.bloomsbury.com/uk/general-ecology-9781350014695/#sthash.6WXDqoeE.dpu

Bridge between worlds: relating position and disposition in the mathematical field

Using ethnographic observations and interview based research I document the production of research mathematics in four European research institutes, interviewing 45 mathematicians from three areas of pure mathematics: topology, algebraic geometry and differential geometry. I use Bourdieu's notions of habitus, field and practice to explore how mathematicians come to perceive and interact with abstract mathematical spaces and constructions. Perception of mathematical reality, I explain, depends upon enculturation within a mathematical discipline. This process of socialisation involves positioning an individual within a field of production. Within a field mathematicians acquire certain structured sets of dispositions which constitute habitus, and these habitus then provide both perspectives and perceptual lenses through which to construe mathematical objects and spaces. I describe how mathematical perception is built up through interactions within three domains of experience: physical spaces, conceptual spaces and discourse spaces. These domains share analogous structuring schemas, which are related through Lakoff and Johnson's notions of metaphorical mappings and image schemas. Such schemas are mobilised during problem solving and proof construction, in order to guide mathematicians' intuitions; and are utilised during communicative acts, in order to create common ground and common reference frames. However, different structuring principles are utilised according to the contexts in which the act of knowledge production or communication take place. The degree of formality, privacy or competitiveness of environments affects the presentation of mathematicians' selves and ideas. Goffman's concept of interaction frame, front-stage and backstage are therefore used to explain how certain positions in the field shape dispositions, and lead to the realisation of different structuring schemas or scripts. I use Sewell's qualifications of Bourdieu's theories to explore the multiplicity of schemas present within mathematicians' habitus, and detail how they are given expression through craftwork and bricolage. I argue that mathematicians' perception of mathematical phenomena are dependent upon their positions and relations. I develop the notion of social space, providing definitions of such spaces and how they are generated, how positions are determined, and how individuals reposition within space through acquisition of capital

Transformation Paradox: A Framework for the Analysis of Politics in Enterprise Transformations

The purpose of this research is to develop a theoretical framework for the analysis of politics in enterprise transformations using a dialectical analysis approach (Hegel, 1989; Heraclitus, 1979; Pinkard, 1988; Skinner, 1978a, 1978b) and conduct an evaluation of the framework validity. The framework is constructed using a dialectical analysis of concepts stemming from the work of Alford and Friedland (1992) and considers four theoretical perspectives: autocratic, bureaucratic, pluralistic, and cognitive. The framework is then validated by means of qualitative metrics and adherence to critical ideology. This research addresses the problem that there is no holistic theoretical framework for the analysis of politics across the systemic, situational, and structural contexts found in enterprise transformations. Politics occurs at multiple levels in the enterprise making it difficult to identify the salient issues that need to be addressed in support of transformation. Transformations can be paradoxical as enterprises revert to the dominant paradigm that affirms present realities rather than developing a critical posture to break the constraining paradigm. The dialectical approach used embraces the power of multiple theoretical perspectives in the transformation process, asserting that theories have power over actions, behaviors, and language. The theoretical framework allows for the simultaneous existence of shifting states of cooperation, frustration, and paradigmatic hegemony over systemic, situational, and structural contexts that embody politics in enterprise transformations. Rough set theory is used to demonstrate the ability of the framework to be adaptive and to evolve based on the inclusion of new data. I conclude that the deployment of an evolving framework of this magnitude may have a significant impact on the management of transformation efforts and suggest new areas of research to further the work

Keys to Play: Music as a Ludic Medium from Apollo to Nintendo

How do keyboards make music playable? Drawing on theories of media, systems, and cultural techniques, Keys to Play spans Greek myth and contemporary Japanese digital games to chart a genealogy of musical play and its animation via improvisation, performance, and recreation. As a paradigmatic digital interface, the keyboard forms a field of play on which the book’s diverse objects of inquiry—from clavichords to PCs and eighteenth-century musical dice games to the latest rhythm-action titles—enter into analogical relations. Remapping the keyboard’s topography by way of Mozart and Super Mario, who head an expansive cast of historical and virtual actors, Keys to Play invites readers to unlock ludic dimensions of music that are at once old and new

Calculating Value: Using and Collecting the Tools of Early Modern Mathematics

Through detailed evaluation of the Science Museum Library’s Rare Books Collection, this thesis explores the use, ownership and subsequent collection of mathematical books produced between 1550 and 1750. Research has been undertaken as part of a Collaborative Doctoral Award between Swansea University and the Science Museum, London, funded by the UK Arts and Humanities Research Council from 1 January 2016 to 31 December 2018. Consisting of close to 1,700 titles published between 1486 and 1800 encompassing the pre-modern classification of mathematics, this subset of the Rare Books Collection represents a remarkable accumulation of the practical and the theoretical across a variety of disciplines and languages. My thesis begins by characterising these mathematical holdings in aggregate, analysing the contents and physical features of the texts therein. Findings are supplemented by examination of accompanying provenance, including bindings, bookplates, and signatures. Discrete case-studies then present key texts as part of their readers’ burgeoning mathematical practice, with chapters focussing on the spread of Ramist pedagogies of arithmetic, geometry, and trigonometry in sixteenth-century Germany; the interconnected use of text, instrument and theory in early modern English intellectual and navigational cultures; and the value attached to the related disciplines of mathematical astronomy and chronology at the University of Cambridge in the late 1690s. The thesis closes with a reconstruction of the library of the clergyman and mathematician, Nathaniel Torporley (1564-1632), tracing the journey of Torporley’s materials to the collection of the antiquarian Robert Brodhead Honeyman (1897-1987) and to the Science Museum thereafter. By placing the Museum’s Library and its holdings in their correct historical contexts, this thesis contributes to our understanding of mathematical culture in the early modern period, to the history of collecting in the modern era, and to the Science Museum’s understanding of its own holdings and of its role as an institutional collector