This volume, with a foreword by Sir Roger Penrose, discusses the foundations of computation in relation to nature. It focuses on two main questions: What is computation? How does nature compute? The contributors are world-renowned experts who have helped shape a cutting-edge computational understanding of the universe. They discuss computation in the world from a variety of perspectives, ranging from foundational concepts to pragmatic models to ontological conceptions and philosophical implications. The volume provides a state-of-the-art collection of technical papers and non-technical essays, representing a field that assumes information and computation to be key in understanding and explaining the basic structure underpinning physical reality. It also includes a new edition of Konrad Zuse's “Calculating Space” (the MIT translation), and a panel discussion transcription on the topic, featuring worldwide experts in quantum mechanics, physics, cognition, computation and algorithmic complexity. The volume is dedicated to the memory of Alan M Turing — the inventor of universal computation, on the 100th anniversary of his birth, and is part of the Turing Centenary celebrations.Contents: Foreword (R Penrose) Preface Acknowledgements Introducing the Computable Universe (H Zenil) Historical, Philosophical & Foundational Aspects of Computation: Origins of Digital Computing: Alan Turing, Charles Babbage, & Ada Lovelace (D Swade) Generating, Solving and the Mathematics of Homo Sapiens. E Post's Views on Computation (L De Mol) Machines (R Turner) Effectiveness (N Dershowitz & E Falkovich) Axioms for Computability: Do They Allow a Proof of Church's Thesis? (W Sieg) The Mathematician's Bias — and the Return to Embodied Computation (S B Cooper) Intuitionistic Mathematics and Realizability in the Physical World (A Bauer) What is Computation? Actor Model versus Turing's Model (C Hewitt) Computation in Nature & the Real World: Reaction Systems: A Natural Computing Approach to the Functioning of Living Cells (A Ehrenfeucht, J Kleijn, M Koutny & G Rozenberg) Bacteria, Turing Machines and Hyperbolic Cellular Automata (M Margenstern) Computation and Communication in Unorganized Systems (C Teuscher) The Many Forms of Amorphous Computational Systems (J Wiedermann) Computing on Rings (G J Martínez, A Adamatzky & H V McIntosh) Life as Evolving Software (G J Chaitin) Computability and Algorithmic Complexity in Economics (K V Velupillai & S Zambelli) Blueprint for a Hypercomputer (F A Doria) Computation & Physics & the Physics of Computation: Information-Theoretic Teleodynamics in Natural and Artificial Systems (A F Beavers & C D Harrison) Discrete Theoretical Processes (DTP) (E Fredkin) The Fastest Way of Computing All Universes (J Schmidhuber) The Subjective Computable Universe (M Hutter) What Is Ultimately Possible in Physics? (S Wolfram) Universality, Turing Incompleteness and Observers (K Sutner) Algorithmic Causal Sets for a Computational Spacetime (T Bolognesi) The Computable Universe Hypothesis (M P Szudzik) The Universe is Lawless or “Pantôn chrêmatôn metron anthrôpon einai” (C S Calude, F W Meyerstein & A Salomaa) Is Feasibility in Physics Limited by Fantasy Alone? (C S Calude & K Svozil) The Quantum, Computation & Information: What is Computation? (How) Does Nature Compute? (D Deutsch) The Universe as Quantum Computer (S Lloyd) Quantum Speedup and Temporal Inequalities for Sequential Actions (M Żukowski) The Contextual Computer (A Cabello) A Gödel-Turing Perspective on Quantum States Indistinguishable from Inside (T Breuer) When Humans Do Compute Quantum (P Zizzi) Open Discussion Section: Open Discussion on A Computable Universe (A Bauer, T Bolognesi, A Cabello, C S Calude, L De Mol, F Doria, E Fredkin, C Hewitt, M Hutter, M Margenstern, K Svozil, M Szudzik, C Teuscher, S Wolfram & H Zenil) Live Panel Discussion (transcription): What is Computation? (How) Does Nature Compute? (C S Calude, G J Chaitin, E Fredkin, A J Leggett, R de Ruyter, T...
