The entropy-based quantum metric

International audienceThe von Neumann entropy S(ˆD ) generates in the space of quantum density matrices ˆD the Riemannian metric ds2 = −d2S(ˆD ), which is physically founded and which characterises the amount of quantum information lost by mixing ˆD and ˆD + dˆD. A rich geometric structure is thereby implemented in quantum mechanics. It includes a canonical mapping between the spaces of states and of observables, which involves the Legendre transform of S(ˆD). The Kubo scalar product is recovered within the space of observables. Applications are given to equilibrium and non equilibrium quantum statistical mechanics. There the formalism is specialised to the relevant space of observables and to the associated reduced states issued from the maximum entropy criterion, which result from the exact states through an orthogonal projection. Von Neumann's entropy specialises into a relevant entropy. Comparison is made with other metrics. The Riemannian properties of the metric ds2 = −d2S(ˆD) are derived. The curvature arises from the non-Abelian nature of quantum mechanics; its general expression and its explicit form for q-bits are given

Readings in the 'New Science': a selective annotated bilbiography

Die vorliegende kommentierte Bibliographie will hauptsächlich Historikern eine Orientierungshilfe für die Literaturfülle zum Thema 'New Science' geben. Die knapp besprochenen Arbeiten sind nach folgenden Themenkomplexen gruppiert: Unentscheidbarkeit, Ungewißheit und Komplexität; Makrostrukturen: Systeme und die humane Dimension; Dynamische Systeme (Spieltheorie, Katastrophentheorie, Chaos, Fraktale Geometrie, Antizipatorische Systeme, Lebende Systeme); Computer (Informationstheorie, Kognitionswisssenschaft und Künstliche Intelligenz); Die Mikro- und die Makrodimensionen; Zeit; Kultur und Erkenntnistheorie. (pmb

Evolutionary Computation

This book presents several recent advances on Evolutionary Computation, specially evolution-based optimization methods and hybrid algorithms for several applications, from optimization and learning to pattern recognition and bioinformatics. This book also presents new algorithms based on several analogies and metafores, where one of them is based on philosophy, specifically on the philosophy of praxis and dialectics. In this book it is also presented interesting applications on bioinformatics, specially the use of particle swarms to discover gene expression patterns in DNA microarrays. Therefore, this book features representative work on the field of evolutionary computation and applied sciences. The intended audience is graduate, undergraduate, researchers, and anyone who wishes to become familiar with the latest research work on this field

Architecture and the creation of worlds

This thesis is an enquiry by creative practice into the academic and aesthetic (avant-garde) practice of architecture. It explores the notion of the virtual as pure potentiality following an event, and defines architecture as the site of such potentiality. (Alain Badiou names event as the moment /encounter which initiates a radical break from a given situation /state of affairs. There are four types of event: artistic, political, scientific and amorous).The thesis follows two parallel strands of enquiry. One, into the material production of the architectural object and topological space, this is titled the actual; and the other, an investigation into the philosophical and antagonistic nature of the virtual, this is titled the virtual. The actual deals with the literature review, methodology, context of study and proposal for (the site of) actual engagement with theory, including a design element (House of the Chinese Mantis); while the virtual explores (through a series of five international and interdisciplinary conference papers) the philosophical problems of emergence. The 'context of study' in the actual centres around the move from the fetish of commodities to seduction and concludes with eroticism, while the body of work in the virtual concentrates on the notions of sovereignty, becoming, and concrete subjectivity.Following the technological practices of the avant-garde between hypersurface theory and catalytic formations in architecture, the thesis rejects the claims of virtual space as the digital space of computer -based design, and of emergence as mimetic and /or algorithm based design. It argues that the virtual is the intangible space of creative unfolding following Bergson and Deleuze, but resists the claim in Deleuze that event is a chance occurring. Also, it resists the claim in Baudrillard that seduction and /or enchanted simulation are event and abandons them to focus on the amorous (one of the four events in Badiou). This creates an inflection in the enquiry, moving the thesis towards Plato and the Renaissance, and a contemporary resurrection in architecture, of the tragic, as concrete manifestation of the amorous encounter.The method of inquiry is structured after the nomadic logic of the War Machine in the philosophy of Deleuze and Guattari, and of the revolutionary nature of fidelity to the scientific event in Badiou, which argues that new knowledge is created by 'revolutions' and from the anomalies and collaborations which arise as a result of such 'detours'; it is a strategy justified by the science historians Feyerabend, Kuhn and Lakatos.The thesis takes the form of two books (the actual and the virtual), and concludes that the avant-garde practice of architecture, with its infinite potentialities is distinct from the bureaucratic or State apparatus of building, and that the commonplace appropriation of the avant-garde by the State, as seen in the institutional recourse to parametrics, appears unproductive and uncreative with regard to knowledge

New Foundation in the Sciences: Physics without sweeping infinities under the rug

It is widely known among the Frontiers of physics, that “sweeping under the rug” practice has been quite the norm rather than exception. In other words, the leading paradigms have strong tendency to be hailed as the only game in town. For example, renormalization group theory was hailed as cure in order to solve infinity problem in QED theory. For instance, a quote from Richard Feynman goes as follows: “What the three Nobel Prize winners did, in the words of Feynman, was to get rid of the infinities in the calculations. The infinities are still there, but now they can be skirted around . . . We have designed a method for sweeping them under the rug. [1] And Paul Dirac himself also wrote with similar tune: “Hence most physicists are very satisfied with the situation. They say: Quantum electrodynamics is a good theory, and we do not have to worry about it any more. I must say that I am very dissatisfied with the situation, because this so-called good theory does involve neglecting infinities which appear in its equations, neglecting them in an arbitrary way. This is just not sensible mathematics. Sensible mathematics involves neglecting a quantity when it turns out to be small—not neglecting it just because it is infinitely great and you do not want it!”[2] Similarly, dark matter and dark energy were elevated as plausible way to solve the crisis in prevalent Big Bang cosmology. That is why we choose a theme here: New Foundations in the Sciences, in order to emphasize the necessity to introduce a new set of approaches in the Sciences, be it Physics, Cosmology, Consciousness etc

The Physicist - Philosophers: The Legacy of James Clerk Maxwell and Herrmann von Helmholtz

One of the most effective, and most mysterious, tools of modern theoretical physics is a mathematical method including what is here called “field theory.” The success of this procedure in unraveling the “zoology” of fundamental particles and their behavior is a marvel. The philosophical context of this marvel is the source of endless academic controversy. The core of the method is a blend of mathematics and description created by “physicist-philosophers,” from Maxwell and Helmholtz to Einstein and Schrödinger. This book tries to unravel the mystery, or at least chronicle it.https://digitalcommons.bard.edu/facbooks/1000/thumbnail.jp

Uncertainty and Managerial Decisions for New Technology-based Ventures

Uncertainty is inherently related to the process of venturing new technologies. Understanding this uncertainty is thus crucial for managerial decisions. Whereas a lot has been written about dealing with uncertainty and decision-making, such as decision theory approaches, in cases of new technologies high levels of uncertainty are still apparent. This is illustrated by such events as the technology boom-bust on the stock exchange in 2000. Alternative methods are called for, and hence is the topic of this thesis. This thesis proposes an alternative way of dealing with the specific uncertainties surrounding new technology-based ventures with the aim to support decision-making. The thesis builds on an extensive literature study in the topic of uncertainty and establishes a conceptual method that uses three elements to approach this uncertainty. Firstly, define uncertainty in a duality. Secondly, applying probabilities instead of causality arguments to understand this uncertainty. Thirdly, exploring such probabilities through experimentation. For practitioners, the result from the experimentation is a process based performance measurement system that allows decision-makers to better predict performance for new technology-based ventures. For academia, this thesis contributes a new conceptual understanding of uncertainty as well as the introduction of a method that combines system engineering with case study research