Books by Karl Sigmund
We list below various books written by Karl Sigmund. We give extracts from reviews and publisher's information for these (where appropriate). The books are listed in chronological order.
- Ergodic Theory on Compact Spaces (1976), by Manfred Denker, Christian Grillenberger and Karl Sigmund.
1.1 Review by: Bill Parry.
Mathematical Reviews MR0457675 (56 #15879)
For the two decades preceding 1960 ergodic theory was a comparatively dormant subject that could be viewed (through the books of Hopf, Halmos and Jacobs for example) as a unity. Since then the subject has grown in popularity, activity and scope, making an overall view nearly impossible except perhaps in survey article form ... The most we can expect in book form are specialised personal accounts and these are appearing regularly. Such is the book under review, which reflects, to a considerable extent, the separate but overlapping interests of three authors. The subject they have chosen is restricted, in that it concerns topological ergodic theory and omits the volatile areas of Bernoulli and loose Bernoulli theory, ergodic number theory, cohomology of group actions, etc. Nevertheless, their work is a welcome addition to the growing number of books on ergodic theory. Students will find in it easy passages to a number of frontier topics and sound foundational material frequently omitted from courses and other sources. ... The wealth of information provided by this timely treatise cannot be conveyed in a short review. Suffice it to say that current ergodic theorists will find the book indispensable.
- Evolutionstheorie und dynamische Systeme (1984), by J Hofbauer and Karl Sigmund.
This book was translated into English with the title The Theory of Evolution and Dynamical Systems. See  below for reviews of the English version.
- The Theory of Evolution and Dynamical Systems (1988), by J Hofbauer and Karl Sigmund.
3.1. From the Publisher:
This textbook is an introduction to dynamical systems and its applications to evolutionary game theory, mathematical ecology, and population genetics. This first English edition is a translation from the authors' successful German edition which has already made an enormous impact on the teaching and study of mathematical biology. The book's main theme is to discuss the solution of differential equations that arise from examples in evolutionary biology. Topics covered include the Hardy-Weinberg law, the Lotka-Volterra equations for ecological models, genetic evolution, aspects of sociobiology, and mutation and recombination. There are numerous examples and exercises throughout and the reader is led up to some of the most recent developments in the field. Thus the book will make an ideal introduction to the subject for graduate students in mathematics and biology coming to the subject for the first time. Research workers in evolutionary theory will also find much of interest here in the application of powerful mathematical techniques to the subject.
3.2. Review by: Alexander Gimelfarb and Steven Orzack.
BioScience 39 (11) (1989), 820-821.
Despite its title, 'The Theory of Evolution and Dynamical Systems' is much more a unified treatment of dynamical systems arising in different areas of evolutionary biology than it is a discussion of evolutionary theory. The virtue of this focus is that it allows one to readily see the mathematical unity of models motivated by distinct biological subjects. The book is divided into two main parts. The first part, an introduction to the qualitative theory of differential and difference equations, is based entirely on examples from biology. ... The second part of the book contains a unified treatment of the dynamical systems discussed in the first part. ... What does one learn from this book? The biologists will learn of the mathematical unity of seemingly distinct biological problems, of the wealth of mathematical complexity hidden behind even relatively simple biological models, and of the mathematical rigour that can be usefully applied in the analysis of such models. The mathematician will learn of the variety of biologically motivated problems still unsolved or not fully analysed.
3.3. Review by: Thomas G Hallam.
SIAM Review 32 (2) (1990), 322-323.
Hofbauer and Sigmund indicate in the Preface that " ... crucial aspects of theoretical biology can only be captured by mathematical modelling; and just as important as the mathematical applications in biology are the biological motivations to mathematics." The maturity of the field of mathematical biology does indeed rest on the interplay between the mathematics and the biology. Any attempt to do justice to both areas requires sincere efforts; it is clear that the authors have invested much effort in this work. It is also evident that this book is written for mathematicians. Even the biologically oriented sections often include models and mathematics that many biologists would find challenging. The book addresses a spectrum of topics ranging from the prebiotic evolution of macromolecules to population genetics, dynamic population, and community ecology, and to game-theoretic modelling of animal behaviour.
3.4. Review by: H Resit Akcakaya.
The Quarterly Review of Biology 64 (4) (1989), 493.
This textbook is an introduction to the use of mathematics in four related areas of biology: population ecology, population genetics, sociobiology and prebiotic molecular evolution. The main emphasis is the analysis of differential equations with examples of their use in models of ecological and evolutionary processes. ... Although the motivation of discussions throughout the book is biological, the book will be more accessible to students of mathematics than to students of biology. It will be very useful and stimulating for mathematics students who want to shift their interest to- wards biology, and it may also be helpful for mathematically oriented students of biology.
3.5. Review by: Sabin Lessard.
American Scientist 79 (2) (1991), 180.
Those interested in dynamical systems with particular reference to evolutionary biology will appreciate this textbook. Some of the most classical results and more recent developments in population genetics, ecology, evolutionary game theory and prebiotic evolution are presented. Special attention is given to the Lotka-Volterra equations and game dynamics. Applications are found for several mathematical techniques, including the Ljapunov functions, the Poincaré maps, the Hopf bifurcations, the Shahshahani gradients, the Perron-Frobenius theory and the Poincaré Bendixson theorem. Throughout the book there are exercises for students and notes for teachers or investigators who are interested in knowing more about the subject. The treatment is clear, and the book is quite appropriate for an advanced course in differential equations and their applications.
3.6. Review by: Gabriela Schranz-Kirlinger.
Mathematical Reviews MR1071180 (91h:92019).
This book is an extended English translation of the 1984 German version (Evolutionstheorie und dynamische Systeme: Mathematische Aspekte der Selektion, 1984). The authors' goal is indicated in the introduction. "It should be (a) an introduction to the theory of dynamical systems (and in particular the qualitative theory of differential equations), based entirely on examples from biology; and (b) a survey of recent developments in four branches of the theory of evolution, namely population genetics, mathematical ecology, prebiotic evolution of macromolecules, and game theoretic modelling of animal behaviour ... " The field of mathematical biology or biomathematics rests on the interplay between mathematics and biology. The authors' position is clear, their main emphasis lies on the first; the book is written by mathematicians for mathematicians. ... The authors' hope "to point out some interesting sights along the way from undergraduate mathematics to current research'' is successfully achieved. More than that, this outstanding work clearly represents biologically motivated mathematics interesting for graduate students in mathematics and biology coming to the subject for the first time, as well as for research workers in evolutionary theory.
- Games of Life: Explorations in Ecology, Evolution, and Behaviour (1994), by Karl Sigmund.
4.1. From the Publisher:
Life is often a matter of gambles, pay-offs, and trade-offs, just like a game. This book takes readers on a tour through the games and computer simulations that are actually helping to advance knowledge in such fields as ecology, evolution, and animal behaviour. Although the book deals with questions of vital importance, like sex and survival, it does so in the lively, entertaining spirit of game-playing. It starts with artificial life and self-replicating automata, a topic ideally suited for a computer-games approach. The book goes on to study pursuit games between predators and prey, and chaotic motion and its role in ecology. Games of chance and statistical paradoxes illuminate the randomness in molecular evolution, while some bizarre double games played by chromosomes help explain the laws of population genetics. Other topics include courtship, ownership, partnership, and brinksmanship-illustrated through the game of poker and computer tournaments. 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 their course. General readers as well as professionals and students in ecological, evolutionary, and behavioural studies will find this a fascinating and informative work.
4.2. Review by: Times Higher Educational Supplement.
Karl Sigmund's 'Games of Life' is a beautifully written and, considering its relative brevity, amazingly comprehensive survey of past and current thinking in "mathematical" evolution. Just as games (at least, the human variety) are supposed to be fun, so too is 'Games of Life' - the witty section headings, the relaxed style and the clarity of the explanations make the book as enjoyable to read as a Marx Brothers film (to which there is a reference in the book) is to watch.
4.3. Review by: Peter Yodzis.
Science, New Series 264 (5156) (1994), 294-295.
There is a style of popular scientific writing that draws its narrative energy from the personalities of a few prominent scientists and the drama that flows from their obsessions. The best of this genre are well worth the attention of students and practitioners of science, but these readers are also well served by something a little meatier, in the manner of George Gamow or Erwin Schrodinger in their "popular" mode. Karl Sigmund's Games of Life is firmly in this latter tradition, though it does contain a few (quite entertaining) biographical asides. The book is a semipopular account of theoretical evolutionary biology, with an emphasis on behavioural phenomena and on game-theoretical methods. The tone is genial and playful. Although the book is about mathematical ideas, Sigmund has opted to avoid explicit mathematics (equations). Presumably this is meant to make the book more palatable to a readership of biologists, but there are a few spots in the book where an equation or two would make the argument a lot more transparent. Sigmund introduces his book with a spirited defence of the use of mathematical thinking in the context of biological problems. He reminds us, for example, that Mendel was a student far less of biology than of mathematics; and later in the book he goes so far as to suggest that Mendel's mathematical training accounts for the otherwise enigmatic circumstance that it was he and not his contemporary Darwin who laid the genetic foundation that was to support Darwin's own ideas. As one is carried along by Sigmund's persuasive account here, nothing seems more natural than to apply mathematical thinking in biology-one can almost imagine the day when a semipopular book on mathematical biology will contain a few equations. For Sigmund, mathematics is the essential tool of the thought experiment, the exploration of the explanatory power of some what if? proposition.
4.4. Review by: Ethan Akin.
The Quarterly Review of Biology 69 (4) (1994), 573-574.
Sigmund knows, and intends to show, that to identify mathematics by solving huge equations is to confuse a practice with tools used therein. Mathematics is better thought of as a style of thinking hinted at with words like "modelling" and "abstraction," which are easier to demonstrate than to describe. This book is a demonstration conducted with very great style indeed. Sigmund's initial description is a bold admission inasmuch as love of mathematics is a perversion sufficiently rare as to render the phrase "popular mathematics book" oxymoronic. His confrontation with the tastes of his prospective readers is deliberate in that he intends to defend as well as to illustrate the use of mathematics in biology. His first chapter provides an explicit argument for the patterns of thinking, which his later chapters illustrate. Sigmund argues for the value of thought experiments. These are usually hypothetical models that are somewhat removed from actual data. It is this a priori character that requires a defence, especially in light of the imperial arrogance shown by some mathematicians as they sail off to colonise neighbouring subjects. For example, Rene Thorn, in the delightful tradition of Cartesian rationalism, suggested that embryologists abandon the problem of morphogenesis to the mathematicians who would, no doubt, solve it in short order.
4.5. Review by: Jeffrey R Lucas.
Ecology 75 (8) (1994), 2468-2469.
There are a number of writers, including Richard Dawkins, Steven Vogel, and Stephen Gould, whose writing style makes their work worth reading just for the prose. Karl Sigmund is another name to add to the list. Sigmund's Games of Life is loosely centred on a fairly eclectic range of biological games, with an intended audience of "potential or actual students and the interested layperson." The book covers inherently mathematical themes but offers only the logic behind the models and their predictions, without any of the math, hence the accessibility to interested laypersons. Sigmund's lucid style and use of historical anecdotes make this book eminently readable. The book doesn't break any new ground, but it is a wonderful introduction to the logic of some of the models that have been developed in evolutionary ecology.
- Evolutionary Games and Population Dynamics (1998), by J Hofbauer and Karl Sigmund.
5.1. From the Publisher:
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 realized 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 programs. In this book the authors investigate the nonlinear dynamics of the self-regulation of social and economic behaviour, and of the closely related interactions among species in ecological communities. Replicator equations describe how successful strategies spread and thereby create new conditions that 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 that 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.
5.2. Review by: Susan Holmes.
Journal of the American Statistical Association 95 (450) (2000), 688.
This book is written by well-known specialists of dynamical systems and their applications to ecology. This presentation takes game theory from Von Neumann's initial setting through John Nash's work on equilibrium seen as a branch of dynamical systems, and explains the applications of game theory to biology. Evolutionary Games and Population Dynamics is definitely a book that requires some mathematical training, and biologists desiring an introduction to the subject would benefit from a more concrete, hands-on book .... Students in applied mathematics, however, will find Evolutionary Games and Population Dynamics exactly along their lines, with just enough applications given to make the equations come to life.
5.3. Review by: Steven D Carroll.
The Quarterly Review of Biology 74 (3) (1999), 347.
In essence, this is a mathematical textbook, the main subjects of which are replicator dynamics and Lotka-Volterra equations. The book is divided into four parts: Dynamical Systems and Lotka-Volterra Equations, Game Dynamics and Replicator Equations, Permanence and Stability, and Population Genetics and Game Dynamics. Each part contains an exhaustive compilation of mathematical theorems, many of which have been added to the literature within the last decade. The book lacks (by design ) extensive biological discussion, so interpretation of these results is generally left to readers. ... Relatively complicated theorems and proofs comprise a large portion of the book, and it is therefore not recommended for those who are not mathematically inclined. In fact, many theorems are stated without proof, and in stead are given as exercises for readers to complete. For the biologist who is mathematically inclined or the mathematician interested in biology, however, this volume is rich in results and likely to provoke stimulating thought.
5.4. Review by: Gabriela Schranz-Kirlinger.
Mathematical Reviews MR1635735 (99h:92027).
The book under review is a very nice further development of its ten-year-old predecessor (The theory of evolution and dynamical systems, 1988) by the authors. Not only has the title been modified, but also the contents have been thoroughly reworked and thus adapted to today's topics of interest in the field of biomathematics. The book is totally restructured and contains much new material, mainly in game theory, especially in its evolutionary and dynamical aspects. Game theory is approached in terms of dynamical systems. ... Summarizing, this book is written in the well-known authors' usual clear, elegant and motivating style.
- Kurt Gödel - The Album (2006), by J Dawson, K Mühlberger and Karl Sigmund.
6.1. From the Publisher:
Time Magazine ranked him among the hundred most important persons of the twentieth century. Harvard University made him an honorary doctor "for the discovery of the most significant mathematical truth of the century". He is generally viewed as the greatest logician since Aristotle. His friend Einstein liked to say that he only went to the Institute to have the privilege of walking back home with Kurt Gödel. And John von Neumann, one of the fathers of the computer, wrote: "Indeed Gödel is absolutely irreplaceable. He is the only mathematician about whom I dare make this assertion." This book wants to give a simple, intuitive and easily digestible introduction to Gödel's life and work, meant for readers interested in the human and cultural aspects of science. Its starting point was the preparations for an exhibition on Kurt Gödel, on the occasion of his hundredth birthday. An exhibition has something of a walk in it, and that's just what we want to offer: a walk with Gödel. Albert Einstein enjoyed such walks very much. So one can enjoy Gödel.
6.2. Review by: Jeremy Gray.
Mathematical Reviews MR2242887 (2007d:01010)
This attractive book, in English and German, is an account of the life of Kurt Gödel in words and pictures. It grew out of preparations for an exhibition on Gödel as part of the commemorations of the 100th anniversary of his birth, and extracts from it have appeared in the April 2006 issue of the Notices of the American Mathematical Society. The authors offer it to readers "interested in the human and cultural aspects of science''. They trace Gödel's life from birth, through school and university, the first of his great discoveries, the highly stressful time of his emigration to Princeton in 1939, and his later work, to his death from inanition in 1978. They show the great impact his work had, document his close friendship with Einstein, and devote a chapter to Gödel's Vienna and the Vienna Circle. In an appendix they provide Gödel's own brief summary of his incompleteness theorem and a longer account by Menger, rightly judging that this is not the occasion for a more detailed account. They provide a rich introduction to the study of Gödel's ideas that will more than answer the question of who Gödel was, that will go some way to answering the question of what he did, and that will stimulate young and not so young readers to find out more.
6.3. Review by: Ralf Schindler.
European Mathematical Society.
A great book! It is at least as valuable as the exhibition that it catalogues. It will be appreciated by anybody who is interested in or curious about Kurt Gödel. The life's work of Gödel ranks among the highest from the point of view of pure science. At the same time it must be seen in the context of the intellectually productive Viennese atmosphere that was present in the first decades of the 20th century and of the following political disaster. The catalogue is divided into three parts: Gödel's life, Gödel's work and Gödel's Vienna. It is beautifully illustrated, with photographs, documents and letters. We have never been given a closer look at the true Gödel; we see a copy of a school report of the eleven-year-old Kurt that exhibits only the best grades, with the only exception being a second best in mathematics! We also see copies of official documents concerning Gödel's PhD and his Habilitation, and we see photographs of Adele, who was seven years older than Kurt and who, according to O Morgenstern, "saved his life".
6.4. Review by: Fernando Q Gouvêa.
Mathematical Association of America.
2006 is Kurt Gödel's centenary year, and this book is a worthy way to celebrate. Based on the catalog for a Gödel exhibit, this "album" contains a wealth of photographs and documents that illustrate the life and ideas of one of the most important mathematicians of the twentieth century. As the title indicates, this is an album: a collection of images, of people, places, and texts, with captions in German and English. There are all sorts of neat things here. Many photographs of Gödel are included, one of which is described as a rare image of the man without his glasses. On page 19, there is a high school report card, in which the grades are the highest possible ("sehr gut") on every subject but one. The one exception, of course, is mathematics, in which his grade is a mere "gut". There are many photos of Gödel's contemporaries, including many of the members of the "Vienna Circle." There is even a note, by the director of the Institute for Advanced Study, in which he decides that the speakers at Gödel's funeral should discuss his work on set theory and on logic, but not his "minor" contribution to general relativity.
6.5. Review by: Wilfried Sieg.
History and Philosophy of Logic 29 (1) (2008), 94-96.
The year 2006 is the centenary of Gödel's birth. The preparation of 'Gödels Jahrhundert', an exhibition shown in Vienna from 11 July to 8 August 2006, was also the starting-point for this book. The book's subtitle 'Das Album - The Album' hints at the richness of the photographic material that forms its backbone: early family photos in Brno, photos taken during Gödel's days in Vienna and Princeton, and reproductions of many fascinating documents. The visual material is surrounded by text in English and German; the text explains its significance and draws frequently illuminating connections. The book is divided into three main parts that follow a Preface by the German poet Hans Magnus Enzensberger and an Introduction; the latter ends with the remarks: 'As he [Gödel] told Hao Wang in one of their long interviews: ''I do not fit into this century''. And yet he left his mark on it, maybe precisely because he remained a stranger.' Perhaps the book's strongest point is that it represents Gödel's strained relationship with his century and illuminates the 'maybe precisely because'. It does so by showing an illustrated history of Gödel's life in the first part, entitled 'Gödels Leben - Go del's Life'. This multi-faceted story takes 89 pages and is followed by 53 pages on 'Gödels Werk - Gödel's Work', an informal discussion of the main subjects of Gödel's research. Finally, there are 35 pages devoted to 'Gödels Wien - Gödel's Vienna', not describing the city, but rather presenting briefly some of Gödel's Viennese contemporaries. This portrait gallery starts with his dissertation advisor Hans Hahn and ends with the remarkable novelist Hermann Broch; somewhat out of place, under the heading 'Gödel's Vienna', are the almost three pages devoted to Enzensberger's 1957 and 1972 attempts to see Gödel in Princeton.
- The Calculus of Selfishness (2010), by Karl Sigmund.
7.1. From the Publisher:
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 analyses to what extent one key facet of human nature - selfishness - can lead to cooperation.
7.2. Review by: Cosma Shalizi.
American Scientist 99 (1) (2011), 87-88.
Since the 1970s, a loose community of theoretical biologists, economists, political scientists, mathematicians and philosophers has been using the tools of evolutionary game theory to try to understand how purely selfish agents can come to cooperate, follow norms and even behave altruistically - to understand when honesty is the best policy. Karl Sigmund has been a leading figure in these efforts, and The Calculus of Selfish ness is his latest attempt at an introduction to the field. In its exposition, the book focuses on reciprocity between self-interested individuals in certain elementary types of interactions. ... Sigmund's mathematical exposition is exemplary. He starts with the presumption that the reader has only rudimentary linear algebra (multiplying vectors by matrices) and some notion of what a differential equation is, and he builds up from there, introducing more advanced concepts and results as needed. He avoids formal proofs and bookkeeping in favour of careful explanations of key points and illustrative calculations. As he teaches evolutionary game theory, Sigmund is also demonstrating how to write about applied mathematics.
7.3. Review by: David Krakauer.
Science, New Series 328 (5981) (2010), 977-978.
In 'The Calculus of Selfishness', Karl Sigmund provides a comprehensive and accessible mathematical exposition of the evolutionary game theory of selfishness. The book should prove accessible to natural and social scientists as its mathematical arguments employ intuition, geometry, and simulation with a minimum of axiomatic formality. The demands on the reader typically involve little more than linear algebra and calculus. For Sigmund (a mathematician at the University of Vienna), in the spirit of Adam Smith, selfishness implies the enlightened self-interest of individuals. The problem that game theory seeks to explain is reciprocity among selfish individuals. After opening the book with a short history, Sigmund structures it through a sequence of games. The first is the prototype of reciprocal gaming, the prisoner's dilemma. In subsequent chapters, he includes player identity and memory, allowing for indirect reciprocity. He then introduces the ultimatum game and, finally, public goods games. This hierarchy of games corresponds to an expansion of the volume of social concepts to include fairness, trust, incentives, sanctions, and moral sentiments.
7.4. Review by: Tom Wenseleers.
The Quarterly Review of Biology 86 (1) (2011), 50-51.
In this excellent new book, mathematician Karl Sigmund gives an account of some of his recent and influential contributions in the field of evolutionary game theory - the study of strategic interactions in animal and human populations via methods drawn from evolutionary biology. Unlike the approach of classical economic game theory, these methods do not assume that individuals act rationally, but rather that individuals who receive the highest payoffs will reproduce or be imitated more than others. Evolutionarily stable strategies - the analogue of traditional Nash equilibria - are then identified as the stable restpoints of such "replicator dynamics." ... Although the book is written in a clear and straightforward way, a full appreciation of most of the chapters will require quite a bit more than the "modicum of elementary mathematics" indicated to be mandatory in the preface. In this respect, it will probably appeal most to people with a relatively good mathematic background, such as economists or theoretical evolutionary biologists.
7.5. Review by: Ross Cressman.
Mathematical Reviews MR2590059 (2011h:91035)
Karl Sigmund and his research collaborators have been at the forefront of the concerted effort over the past twenty years to explain the evolution of cooperation. His book, The calculus of selfishness, explores theoretical explanations for the prevalence of cooperative behaviour in human society through the analysis of evolutionary game dynamics for games that model social dilemmas. ... Sigmund has also done an admirable job of motivating the material and making it accessible for the non-expert who is interested in theories to explain the evolution of cooperation.
- Sie nannten sich Der Wiener Kreis - Exaktes Denken am Rand des Untergangs (2015), by Karl Sigmund.
An English translation was published in 2017. See  for some information.
- Exact Thinking in Demented Times: the Vienna Circle and the Epic Quest for the Foundations of Science (2017), by Karl Sigmund.
9.1. From the Publisher:
A dazzling group biography of the early twentieth-century thinkers who transformed the way the world thought about math and science. 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.
9.2. Review by: The Economist.
The Economist (13 January 2018).
On October 21 1916 Friedrich Adler, a theoretical physicist turned socialist politician, went to a famous restaurant in Vienna and ate a three-course lunch. Having lingered over coffee, he went up to Karl von Stürgkh, the imperial prime minister, who was sitting at a nearby table, and shot him several times with a pistol, killing him. Adler, the son of the legendary founder of Austro-Hungarian social democracy, calmly waited to be arrested. Something had to be done to change the general way of thinking, he claimed, and he had done it. At first condemned to death, he was pardoned two years later. When the Nazis came to power in Austria, Adler, by then the secretary of the Socialist Workers' International, held urgent meetings with other socialist politicians to work out a common strategy. During one of these meetings, an emotional Adler rambled on, seemingly unable to come to the point. "He shoots better than he talks," one French delegate remarked drily. "Exact Thinking in Demented Times", Karl Sigmund's fond and knowledgeable exploration of the ideas and members of the legendary Vienna circle between the two world wars, contains stark warnings not only about demented times, but also about the possible costs of exact thinking.
- Games of Life: Explorations in Ecology, Evolution, and Behaviour (2017), by Karl Sigmund.
This is an updated edition of  with a new additional chapter entitled 'Morality play'.
10.1. From the Publisher:
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 modelling to evolution, sex, animal behaviour, and aggression in Games of Life, which was included in Ian Stewart's "Top 10 Popular Mathematics Books" in the Guardian. 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 behaviour. 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.