In this thought-provoking book Küppers, an internationally renowned physicist, philosopher and theoretical biologist, addresses a number of science's deepest questions: Can physics advance to the origin of all things and explain the unique phenomena of life, time and history? Are there unsolvable enigmas of the world? How did life originate? Is language a general phenomenon of Nature? What is time? Is it possible to express the history of the world in formulae? Where is science leading us? These and other provocative questions essential for a deeper understanding of the world are treated here in a refreshing and stimulating manner.

This volume discusses the foundations of computation in relation to nature. It focuses on two main questions: What is computation? and How does nature compute?

Computability has played a crucial role in mathematics and computer science, leading to the discovery, understanding and classification of decidable/undecidable problems, paving the way for the modern computer era, and affecting deeply our view of the world. Recent new paradigms of computation, based on biological and physical models, address in a radically new way questions of efficiency and challenge assumptions about the so-called Turing barrier.This volume addresses various aspects of the ways computability and theoretical computer science enable scientists and philosophers to deal with mathematical and real-world issues, covering problems related to logic, mathematics, physical processes, real computation and learning theory. At the same time it will focus on different ways in which computability emerges from the real world, and how this affects our way of thinking about everyday computational issues./a

Computability theory originated with the seminal work of Gödel, Church, Turing, Kleene and Post in the 1930s. This theory includes a wide spectrum of topics, such as the theory of reducibilities and their degree structures, computably enumerable sets and their automorphisms, and subrecursive hierarchy classifications. Recent work in computability theory has focused on Turing definability and promises to have far-reaching mathematical, scientific, and philosophical consequences. Written by a leading researcher, Computability Theory provides a concise, comprehensive, and authoritative introduction to contemporary computability theory, techniques, and results. The basic concepts and techniques of computability theory are placed in their historical, philosophical and logical context. This presentation is characterized by an unusual breadth of coverage and the inclusion of advanced topics not to be found elsewhere in the literature at this level. The book includes both the standard material for a first course in computability and more advanced looks at degree structures, forcing, priority methods, and determinacy. The final chapter explores a variety of computability applications to mathematics and science. Computability Theory is an invaluable text, reference, and guide to the direction of current research in the field. Nowhere else will you find the techniques and results of this beautiful and basic subject brought alive in such an approachable and lively way.

The World Wide Web is truly astounding. It has changed the way we interact, learn and innovate. It is the largest sociotechnical system humankind has created and is advancing at a pace that leaves most in awe. It is an unavoidable fact that the future of the world is now inextricably linked to the future of the Web. Almost every day it appears to change, to get better and increase its hold on us. For all this we are starting to see underlying stability emerge. The way that Web sites rank in terms of popularity, for example, appears to follow laws with which we are familiar. What is fascinating is that these laws were first discovered, not in fields like computer science or information technology, but in what we regard as more fundamental disciplines like biology, physics and mathematics. Consequently the Web, although synthetic at its surface, seems to be quite 'natural' deeper down, and one of the driving aims of the new field of Web Science is to discover how far down such ’naturalness’ goes. If the Web is natural to its core, that raises some fundamental questions. It forces us, for example, to ask if the central properties of the Web might be more elemental than the truths we cling to from our understandings of the physical world. In essence, it demands that we question the very nature of information. Understanding Information and Computation is about such questions and one possible route to potentially mind-blowing answers.

A unique resource exploring the nature of computers and computing, and their relationships to the world. Philosophy of Computer Science is a university-level textbook designed to guide readers through an array of topics at the intersection of philosophy and computer science. Accessible to students from either discipline, or complete beginners to both, the text brings readers up to speed on a conversation about these issues, so that they can read the literature for themselves, form their own reasoned opinions, and become part of the conversation by contributing their own views. Written by a highly qualified author in the field, the book looks at some of the central questions in the philosophy of computer science, including: What is philosophy? (for readers who might be unfamiliar with it) What is computer science and its relationship to science and to engineering? What are computers, computing, algorithms, and programs?(Includes a line-by-line reading of portions of Turing’s classic 1936 paper that introduced Turing Machines, as well as discussion of the Church-Turing Computability Thesis and hypercomputation challenges to it) How do computers and computation relate to the physical world? What is artificial intelligence, and should we build AIs? Should we trust decisions made by computers? A companion website contains annotated suggestions for further reading and an instructor’s manual. Philosophy of Computer Science is a must-have for philosophy students, computer scientists, and general readers who want to think philosophically about computer science.

How computers simulate cities and how they are also being embedded in cities, changing our behavior and the way in which cities evolve. At every stage in the history of computers and communications, it is safe to say we have been unable to predict what happens next. When computers first appeared nearly seventy-five years ago, primitive computer models were used to help understand and plan cities, but as computers became faster, smaller, more powerful, and ever more ubiquitous, cities themselves began to embrace them. As a result, the smart city emerged. In The Computable City, Michael Batty investigates the circularity of this peculiar evolution: how computers and communications changed the very nature of our city models, which, in turn, are used to simulate systems composed of those same computers. Batty first charts the origins of computers and examines how our computational urban models have developed and how they have been enriched by computer graphics. He then explores the sequence of digital revolutions and how they are converging, focusing on continual changes in new technologies, as well as the twenty-first-century surge in social media, platform economies, and the planning of the smart city. He concludes by revisiting the digital transformation as it continues to confound us, with the understanding that the city, now a high-frequency twenty-four-hour version of itself, changes our understanding of what is possible.

This book constitutes the refereed proceedings of the 6th International Conference on Theory and Applications of Models of Computation, TAMC 2009, held in Changsha, China in May 2009. The 39 full papers presented together with 7 invited papers as well as 3 plenary talks were selected from 86 submissions. The papers address the three main themes of the conference which were Computability, Complexity, and Algorithms. The conference aimed to bring together researchers with interests in theoretical computer science, algorithmic mathematics, and applications to the physical sciences.

Computer scientists, mathematicians, and philosophers discuss the conceptual foundations of the notion of computability as well as recent theoretical developments. In the 1930s a series of seminal works published by Alan Turing, Kurt Gödel, Alonzo Church, and others established the theoretical basis for computability. This work, advancing precise characterizations of effective, algorithmic computability, was the culmination of intensive investigations into the foundations of mathematics. In the decades since, the theory of computability has moved to the center of discussions in philosophy, computer science, and cognitive science. In this volume, distinguished computer scientists, mathematicians, logicians, and philosophers consider the conceptual foundations of computability in light of our modern understanding. Some chapters focus on the pioneering work by Turing, Gödel, and Church, including the Church-Turing thesis and Gödel's response to Church's and Turing's proposals. Other chapters cover more recent technical developments, including computability over the reals, Gödel's influence on mathematical logic and on recursion theory and the impact of work by Turing and Emil Post on our theoretical understanding of online and interactive computing; and others relate computability and complexity to issues in the philosophy of mind, the philosophy of science, and the philosophy of mathematics. Contributors Scott Aaronson, Dorit Aharonov, B. Jack Copeland, Martin Davis, Solomon Feferman, Saul Kripke, Carl J. Posy, Hilary Putnam, Oron Shagrir, Stewart Shapiro, Wilfried Sieg, Robert I. Soare, Umesh V. Vazirani

A research-based guide to political psychology that is filled with critical arguments from noted experts Political Psychology is solidly grounded in empirical research and critical arguments. The text puts the emphasis on alternative approaches to psychological enquiry that challenge our traditional assumptions about the world. With contributions from an international panel of experts, the text contains a meaningful exchange of ideas that draw on the disciplines of social psychology, sociology, history, media studies and philosophy. This important text offers a broader understanding of the different intellectual positions that academics may take towards political psychology. Comprehensive in scope Political Psychology provides a historical context to the subject and offers a critical history of common research methods. The contributors offer insight on political thought in psychology, the politics of psychological language, narrating as political action, political decision-making and much more. This important text: Offers contributions from a panel of international experts on the topic Includes a review of some political ideas associated with the work of Karl Marx, Erich Fromm, R.D. Laing, Michel Foucault and others Presents information on prejudice, stereotypes and discrimination in the context of mass migration Reviews a wide range of relevant topics such as identity, social exclusion and foreign policy and more Contains questions for group debate and discussion at the end of each chapter Written for academics and students of political psychology, Political Psychology is a comprehensive resource that includes contributions from experts in a variety of fields and disciplines.