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Die Beiträge dieses Bandes, der aus dem ersten Symposium des ”Forum on Sustainable Technological Development in a Globalising World“ in Budapest hervorgegangen ist, widmen sich zwei Problemstellungen: Erstens der Möglichkeit rationaler Entscheidungen im Bereich technischer Entwicklung unter den Bedingungen von Ungewißheit (”uncertainty“), d.h. dem Verständnis von, dem Leben in und dem Umgang mit einer ”ungewissen“ Welt. Zweitens setzen sie sich mit den Perspektiven technischer Innovationen in einem sich wandelnden sozialen Umfeld auseinander, vorrangig aus der Perspektive ökologischer Nachhaltigkeit und ihrer sozialen Voraussetzungen. Im Mittelpunkt stehen dabei die Themen: ...
Grassmann Algebra Volume 1: Foundations Exploring extended vector algebra with Mathematica Grassmann algebra extends vector algebra by introducing the exterior product to algebraicize the notion of linear dependence. With it, vectors may be extended to higher-grade entities: bivectors, trivectors, … multivectors. The extensive exterior product also has a regressive dual: the regressive product. The pair behaves a little like the Boolean duals of union and intersection. By interpreting one of the elements of the vector space as an origin point, points can be defined, and the exterior product can extend points into higher-grade located entities from which lines, planes and multiplanes can be...
The interdependency of technology and communication presents theoreticians as well as practitioners with a wide range of problems. Among the topics discussed in this interdisciplinary volume are: technological knowledge in text and context in combination with cognitive and social conditions, knowledge transfer beyond languages and cultures, the influence of the world wide web on social communities.
A new reading of Hegel’s Science of Logic through the history of European mathematics. Conceptual Harmonies develops an original account of G. W. F. Hegel’s perplexing Science of Logic from a simple insight: philosophical and mathematical thought have shaped each other since classical times. Situating Science of Logic within the rise of modern mathematics, Redding stresses Hegel’s attention to Pythagorean ratios, Platonic reason, and Aristotle’s geometrically inspired logic. He then explores how later traditions shaped Hegel’s world, through both Leibniz and new forms of algebraic geometry. This enlightening reading recovers an overlooked stream in Hegel’s philosophy that remains, Redding argues, important for contemporary conceptions of logic.
This edited volume explores the previously underacknowledged 'pre-history' of mathematical structuralism, showing that structuralism has deep roots in the history of modern mathematics. The contributors explore this history along two distinct but interconnected dimensions. First, they reconsider the methodological contributions of major figures in the history of mathematics. Second, they re-examine a range of philosophical reflections from mathematically-inclinded philosophers like Russell, Carnap, and Quine, whose work led to profound conclusions about logical, epistemological, and metaphysic.
On the occasion of the 200th anniversary of the birth of Hermann Graßmann (1809-1877), an interdisciplinary conference was held in Potsdam, Germany, and in Graßmann's hometown Szczecin, Poland. The idea of the conference was to present a multi-faceted picture of Graßmann, and to uncover the complexity of the factors that were responsible for his creativity. The conference demonstrated not only the very influential reception of his work at the turn of the 20th century, but also the unexpected modernity of his ideas, and their continuing development in the 21st century. This book contains 37 papers presented at the conference. They investigate the significance of Graßmann's work for philos...
An examination of what can be learned by looking at the journals and diaries of Jews living during the Holocaust. What are the effects of radical oppression on the human psyche? What happens to the inner self of the powerless and traumatized victim, especially during times of widespread horror? In this bold and deeply penetrating book, Amos Goldberg addresses diary writing by Jews under Nazi persecution. Throughout Europe, in towns, villages, ghettos, forests, hideouts, concentration and labor camps, and even in extermination camps, Jews of all ages and of all cultural backgrounds described in writing what befell them. Goldberg claims that diary and memoir writing was perhaps the most import...
The author defines “Geometric Algebra Computing” as the geometrically intuitive development of algorithms using geometric algebra with a focus on their efficient implementation, and the goal of this book is to lay the foundations for the widespread use of geometric algebra as a powerful, intuitive mathematical language for engineering applications in academia and industry. The related technology is driven by the invention of conformal geometric algebra as a 5D extension of the 4D projective geometric algebra and by the recent progress in parallel processing, and with the specific conformal geometric algebra there is a growing community in recent years applying geometric algebra to applic...
"The stars of the latest book by award-winning science writer and mathematician Robyn Arianrhod are unlikely celebrities--vectors and tensors. If you took a high school physics course, the word "vector" might remind you of the mathematics needed to determine forces on an amusement park ride, say; or of cross products, a special kind of multiplication using a bespoke table and a right-hand rule. You might also remember the introductory definition of a vector as a quantity that has magnitude and (this is the key) direction. Velocity--for example, 25 miles per hour northwest--is a vector; speed, such as 25 miles per hour, is not. Put another way, a velocity vector in space contains not one numb...