Beggining of Infinity Deutsch David

The concept of infinity is one of the most important, and at the same time, one of the most mysterious concepts of science. Already in antiquity many philosophers and mathematicians pondered over its contradictory nature. In mathematics, the contradictions connected with infinity intensified after the creation, at the end of the 19th century, of the theory of infinite sets and the subsequent discovery, soon after, of paradoxes in this theory. At the time, many scientists ignored the paradoxes and used set theory extensively in their work, while others subjected set-theoretic methods in mathematics to harsh criticism. The debate intensified when a group of French mathematicians, who wrote under the pseudonym of Nicolas Bourbaki, tried to erect the whole edifice of mathematics on the single notion of a set. Some mathematicians greeted this attempt enthusiastically while others regarded it as an unnecessary formalization, an attempt to tear mathematics away from life-giving practical applications that sustain it. These differences notwithstanding, Bourbaki has had a significant influence on the evolution of mathematics in the twentieth century. In this book we try to tell the reader how the idea of the infinite arose and developed in physics and in mathematics, how the theory of infinite sets was constructed, what paradoxes it has led to, what significant efforts have been made to eliminate the resulting contradictions, and what routes scientists are trying to find that would provide a way out of the many difficulties.

The concept of infinity is one of the most important, and at the same time, one of the most mysterious concepts of science. Already in antiquity many philosophers and mathematicians pondered over its contradictory nature. In mathematics, the contradictions connected with infinity intensified after the creation, at the end of the 19th century, of the theory of infinite sets and the subsequent discovery, soon after, of paradoxes in this theory. At the time, many scientists ignored the paradoxes and used set theory extensively in their work, while others subjected set-theoretic methods in mathematics to harsh criticism. The debate intensified when a group of French mathematicians, who wrote under the pseudonym of Nicolas Bourbaki, tried to erect the whole edifice of mathematics on the single notion of a set. Some mathematicians greeted this attempt enthusiastically while others regarded it as an unnecessary formalization, an attempt to tear mathematics away from life-giving practical applications that sustain it. These differences notwithstanding, Bourbaki has had a significant influence on the evolution of mathematics in the twentieth century. In this book we try to tell the reader how the idea of the infinite arose and developed in physics and in mathematics, how the theory of infinite sets was constructed, what paradoxes it has led to, what significant efforts have been made to eliminate the resulting contradictions, and what routes scientists are trying to find that would provide a way out of the many difficulties.

The concept of infinity is one of the most important, and at the same time, one of the most mysterious concepts of science. Already in antiquity many philosophers and mathematicians pondered over its contradictory nature. In mathematics, the contradictions connected with infinity intensified after the creation, at the end of the 19th century, of the theory of infinite sets and the subsequent discovery, soon after, of paradoxes in this theory. At the time, many scientists ignored the paradoxes and used set theory extensively in their work, while others subjected set-theoretic methods in mathematics to harsh criticism. The debate intensified when a group of French mathematicians, who wrote under the pseudonym of Nicolas Bourbaki, tried to erect the whole edifice of mathematics on the single notion of a set. Some mathematicians greeted this attempt enthusiastically while others regarded it as an unnecessary formalization, an attempt to tear mathematics away from life-giving practical applications that sustain it. These differences notwithstanding, Bourbaki has had a significant influence on the evolution of mathematics in the twentieth century. In this book we try to tell the reader how the idea of the infinite arose and developed in physics and in mathematics, how the theory of infinite sets was constructed, what paradoxes it has led to, what significant efforts have been made to eliminate the resulting contradictions, and what routes scientists are trying to find that would provide a way out of the many difficulties.

The present anthology, edited by Marcel Herbst, is partially based on a conference, held in 2009, to reflect on the legacy of Ben-David, and contains a selection of substantially revised papers, plus four contributions specifically written for this volume. The book focuses on three major lines of Ben-David’s research, namely “Center and Periphery” (Part I), “Role and Ethos” (Part II), and “Organization and Growth” (Part III). In addition, comprehensive introductory (“Prologue”) and concluding chapters (“Epilogue”, Part IV) by Marcel Herbst are provided. The volume addresses the following disciplines: higher education, history and sociology of science, philosophy of science, history of medicine, public administration, policy studies, Jewish studies, and economics.

…von geladen bis explosiv, von gefährlich bis wohlriechend! Die 2. Auflage des erfolgreichen Wörterbuchs der Chemie von Cole mit nunmehr 32.500 Begriffen aus allen Bereichen der Allgemeinen und Theoretischen Chemie, von Anorganik zur Organik, der Physikalischen Chemie, Biochemie, Nuklearchemie und Polymerchemie. Auch Begrifflichkeiten von Geräten, Methoden oder aus der Analytik werden in beiden Sprachen zur Verfügung gestellt. Das Wörterbuch der Chemie ist ein unentbehrlicher Begleiter für Wissenschaftler, Übersetzer, Dozenten und Studenten, Lehrer und Schüler, die sich zwischen Reagenzglas, Bunsenbrenner und „Hightech-Synthesechemie“ ganz zu Hause fühlen.Thematische Begriffsfelder (clusters) ermöglichen die zusammenhängende Erschließung eines Themas und erleichtern die Arbeit beim Übersetzen.

A bold and all-embracing exploration of the nature and progress of knowledge from one of today's great thinkers.