Karl Sigmund

Redan de gamla grekerna visste att matematik och filosofi hör ihop. Även om man idag inte automatiskt räknar matematiken och filosofin till samma gren på kunskapens träd, är de tätt förbundna genom historien. I sin bok Tankens geometri utforskar matematikern och författaren Karl Sigmund idéhistoriens fruktbara möten mellan matematik och filosofi: hur spelteori hör ihop med moralfilosofi, hur den moderna statistiken utvecklades parallellt med kunskapsteorin och hur jakten på matematikens logik har inspirerat till filosofins allra djupaste spörsmål. Det är en idérik hyllning till det mänskliga förnuftets förmåga att dansa mellan logik, mening och kritik.

"Let no one ignorant of geometry enter here," Plato warned would-be philosophers. Mathematician Karl Sigmund agrees.In The Waltz of Reason, he shows how mathematics and philosophy together have shaped our understanding of space, chance, logic, cooperation, voting, and the social contract. Sigmund shows how game theory is integral to moral philosophy, how statistics shaped the meaning of reason, and how the search for a logical basis for math leads to deep questions about the nature of truth itself. But this is no dry tome: Sigmund's wit and humour shine as brightly as his erudition.The Waltz of Reason is an engrossing history of ideas as vibrant as a ballroom full of dancers, one that empowers as it entertains, following the complex and occasionally dizzying steps of the thinkers who have moulded our thought and founded our world.

Dieses Buch zeichnet Geschichte und Denkansätze des Wiener Kreises nach, des Gelehrtenzirkels, der aus dem Geistesleben des 20. Jahrhunderts nicht wegzudenken ist. Anknüpfend an Russell und Einstein versucht ein Team von Mathematikern, Naturwissenschaftlern und Philosophen die Grundlagen einer wissenschaftlichen Weltauffassung zu legen, im scharfen Gegenwind der reaktionären Politik der Zwischenkriegsjahre. Anschaulich, einfach und einprägsam stellt Karl Sigmund eine der spannendsten Episoden der radikalen Moderne dar - einer Episode, die vom Nationalsozialismus zerstört wurde, aber im angelsächsischen Exil reiche Früchte trug. Viele der damals angerissenen Fragen haben heute noch ihre Auswirkungen: Es führt eine Linie von der symbolischen Logik Carnaps und Gödels zur Informatik, und die wissenschaftliche Weltauffassung ist so selbstverständlich geworden, dass wir sie kaum mehr wahrnehmen. Ein Buch für alle an der Kulturgeschichte des 20. Jahrhunderts Interessierten, dasnaturwissenschaftlich und geisteswissenschaftlich orientierte Leserinnen und Leser in gleichem Maß anspricht. Die zweite Auflage enthält viel neues Material , etwa über die sensationell spannende Flucht Otto Neuraths über den Ärmelkanal, oder über die Laufbahnen von Friedrich Adler und Otto Pölzl (der„Leibpsychiater“), die den Wiener Kreis über Jahrzehnte begleiteten. Auch sind wichtige Seiten über Einstein, Turing und Brouwer dazugekommen. Douglas Hofstadter, der Autor von "Gödel, Escher, Bach", hat ein Nachwort zu dieser Neuauflage verfasst.

Inspired by Albert Einstein's theory of relativity and Bertrand Russell and David Hilbert's pursuit of the fundamental rules of mathematics, some of the most brilliant minds of the generation came together in post-World War I Vienna to present the latest theories in mathematics, science, and philosophy and to build a strong foundation for scientific investigation. Composed of such luminaries as Kurt Gödel and Rudolf Carnap, and stimulated by the works of Ludwig Wittgenstein and Karl Popper, the Vienna Circle left an indelible mark on science. Exact Thinking in Demented Times tells the often outrageous, sometimes tragic, and never boring stories of the men who transformed scientific thought. A revealing work of history, this landmark book pays tribute to those who dared to reinvent knowledge from the ground up.

"A book accessible to all readers, whatever their level of numeracy ... an excellent introduction to what theoretical biologists get up to in trying to understand evolutionary and ecological ideas." ― Nature Why are there only two sexes? Why do stags restrain their aggression in the middle of a fight? Can it ever pay to be nice in a world of selfish individualists? The answers, according to this informative and enjoyable volume, can often be found in games like hide and seek, poker, and the prisoner's dilemma. Author Karl Sigmund applies the ideas and methods of game theory and mathematical modeling to evolution, sex, animal behavior, and aggression in Games of Life, which was included in Ian Stewart's "Top 10 Popular Mathematics Books" in the Guardian (1/18/2012). Starting with artificial life and self-replicating machines, the book examines pursuit games between predators and prey and draws parallels between games of chance and the randomness of molecular evolution. Other topics include the bizarre double games played by chromosomes and applications of game theory to animal behavior. Key topics appear at the start of each chapter, and endnotes provide references for readers wishing to seek out further information. This playful approach to understanding evolution and its central issues of sex, survival, conflict, and cooperation offers a captivating modern perspective on matters of life and death.

Detta är en berättelse om mord och självmord, antisemitism, passion och nervösa sammanbrott som drivs av eldiga kontroverser och djupa filosofiska meningsskjiljaktigheter. I början av 1900-talet hade Wien en central roll inom filosofin. En grupp filosofer som gick under namnet Wienkretsen träffades regelbundet för att diskutera frågor om sanning, kunskap och verklighetens natur. Bland medlemmarna fanns bland annat Moritz Schlick, Rudolf Carnap, Otto Neurath, Olga Hahn-Neurath och Kurt Gödel som i dialog med Ludwig Wittgenstein och Karl Popper formulerande grunden till 1900-talets analytiska filosofi och vetenskapsfilosofi. Trots att det finns flera biografier om de inblandade filosoferna är detta är den första boken som skildrar hela den dramatiska historien med alla dess förvecklingar inklusive kretsens upplösande i och med mordet på Moritz Schlick. Wienkretsen är en episk krönika, snarare än en bukett av biografier.

How does cooperation emerge among selfish individuals? When do people share resources, punish those they consider unfair, and engage in joint enterprises? These questions fascinate philosophers, biologists, and economists alike, for the "invisible hand" that should turn selfish efforts into public benefit is not always at work. The Calculus of Selfishness looks at social dilemmas where cooperative motivations are subverted and self-interest becomes self-defeating. Karl Sigmund, a pioneer in evolutionary game theory, uses simple and well-known game theory models to examine the foundations of collective action and the effects of reciprocity and reputation. Focusing on some of the best-known social and economic experiments, including games such as the Prisoner's Dilemma, Trust, Ultimatum, Snowdrift, and Public Good, Sigmund explores the conditions leading to cooperative strategies. His approach is based on evolutionary game dynamics, applied to deterministic and probabilistic models of economic interactions. Exploring basic strategic interactions among individuals guided by self-interest and caught in social traps, The Calculus of Selfishness analyzes to what extent one key facet of human nature--selfishness--can lead to cooperation.

How does cooperation emerge among selfish individuals? When do people share resources, punish those they consider unfair, and engage in joint enterprises? These questions fascinate philosophers, biologists, and economists alike, for the "invisible hand" that should turn selfish efforts into public benefit is not always at work. The Calculus of Selfishness looks at social dilemmas where cooperative motivations are subverted and self-interest becomes self-defeating. Karl Sigmund, a pioneer in evolutionary game theory, uses simple and well-known game theory models to examine the foundations of collective action and the effects of reciprocity and reputation. Focusing on some of the best-known social and economic experiments, including games such as the Prisoner's Dilemma, Trust, Ultimatum, Snowdrift, and Public Good, Sigmund explores the conditions leading to cooperative strategies. His approach is based on evolutionary game dynamics, applied to deterministic and probabilistic models of economic interactions. Exploring basic strategic interactions among individuals guided by self-interest and caught in social traps, The Calculus of Selfishness analyzes to what extent one key facet of human nature--selfishness--can lead to cooperation.

Time Magazine reihte ihn unter die hundert wichtigsten Personen des zwanzigsten Jahrhunderts. Die Harvard University verlieh ihm das Ehrendoktorat fur die Entdeckung "der bedeutsamsten mathematischen Wahrheit des Jahrhunderts". Er gilt allgemein als der grosste Logiker seit Aristoteles. Sein Freund Einstein ging, nach eigener Aussage, nur deshalb ans Institut, um Godel auf dem Heimweg begleiten zu durfen. Und John von Neumann, einer der Vater des Computers, schrieb: "Godel ist tatsachlich absolut unersetzlich. Er ist der einzige Mathematiker, von dem ich das zu behaupten wage." Dieses Buch ist eine leichtverdauliche, einfache und anschauliche Einfuhrung in Godels Leben und Werk, gedacht fur jene, die sich fur die menschlichen und kulturellen Aspekte der Wissenschaft interessieren. Ausgangspunkt des Buches waren die Vorbereitungen zu einer Ausstellung uber Kurt Godel aus Anlass seines hundertsten Geburtstags. Eine Ausstellung hat etwas von einem Spaziergang an sich, und gerade das wollen wir bieten: einen Spaziergang mit Godel. Albert Einstein genoss solche Spaziergange sehr. Man kann also Godel geniessen.

Karl Menger, one of the founders of dimension theory, belongs to the most original mathematicians and thinkers of the twentieth century. He was a member of the Vienna Circle and the founder of its mathematical equivalent, the Viennese Mathematical Colloquium. Both during his early years in Vienna, and after his emigration to the United States, Karl Menger made significant contributions to a wide variety of mathematical fields, and greatly influenced some of his colleagues. The Selecta Mathematica contain Menger's major mathematical papers, based on a personal selection by himself out of his extensive writings. They deal with topics as diverse as topology, geometry, analysis and algebra, as well as writings on economics, sociology, logic, philosophy and mathematical results. The two volumes are a monument to the diversity and originality of Menger's ideas.

Die von Karl Menger und seinen Mitarbeitern (darunter Kurt Godel) herausgegebenen Ergebnisse eines Mathematischen Kolloquiums zahlen zu den wichtigsten Quellenwerken der Wissenschafts- und Geistesgeschichte der Zwischenkriegszeit, mit bahnbrechenden Beitragen von Menger, Godel, Tarski, Wald, John von Neumann und vielen anderen. In diesem Band liegt der Inhalt erstmals gesammelt vor. Der Nobelpreistrager Gerard Debreu schrieb die Einleitung, die Kommentare wurden vom Logiker und Godel-Biographen John Dawson jr., dem Topologen Ryszard Engelking und dem Wirtschaftstheoretiker Werner Hildenbrand verfasst.Auberdem enthalt der Band einen biographischen Aufsatz uber Karl Menger sowie einen von Menger verfassten Uberblick uber die wichtigsten topologischen und geometrischen Arbeiten des Kolloquiums.

Every form of behaviour is shaped by trial and error. Such stepwise adaptation can occur through individual learning or through natural selection, the basis of evolution. Since the work of Maynard Smith and others, it has been realised how game theory can model this process. Evolutionary game theory replaces the static solutions of classical game theory by a dynamical approach centred not on the concept of rational players but on the population dynamics of behavioural programmes. In this book the authors investigate the nonlinear dynamics of the self-regulation of social and economic behaviour, and of the closely related interactions between species in ecological communities. Replicator equations describe how successful strategies spread and thereby create new conditions which can alter the basis of their success, i.e. to enable us to understand the strategic and genetic foundations of the endless chronicle of invasions and extinctions which punctuate evolution. In short, evolutionary game theory describes when to escalate a conflict, how to elicit cooperation, why to expect a balance of the sexes, and how to understand natural selection in mathematical terms.

Life is often a matter of gambles, pay-offs, and trade-offs, just like a game. This book takes us on a tour through the games and computer simulations that are helping us to understand the ecology, evolution, and behaviour of real life - from cat and mouse to cellular automata, from the battle of the sexes to artificial life, from poker to the prisoner's dilemma. No other book explains so well why scientific observations and insights can be structured as the rules of a survival game, and what happens when they are assembled on a computer or in the mind and allowed to run. With a delightful personal style, the author specifically looks at genetics, population ecology, evolution, and animal behaviour and discusses the often surprising outcomes when the name of the game is life.