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 Toffoli & S Wolfram)*

*Zuse's Calculating Space:*- Calculating Space (
*Rechnender Raum*) *(K Zuse)* *Afterword to Konrad Zuse's Calculating Space (A German & H Zenil)*

**Readership:** Graduate students who are specialized researchers in computer science, information theory, quantum theory and modern philosophy and the general public who are interested in these subject areas.