With a foreword by Sir Roger Penrose, my new volume A Computable Universe has been published by World Scientific and the Imperial College Press after my bestseller Randomness Through Computation in 2011. A Computable Universe: Understanding and Exploring Nature as Computation, introduces the views of the pioneers in the computable universe view of the world and some of its strongest opponents (including Penrose himself).

In the context of the Alan Turing Year, the book discusses the foundations of computation in relation to nature.

**What is computation?****How does nature compute?**

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, prepared by Adrian German from Indiana University Bloomington and myself, of Konrad Zuse’s “**Calculating Space**” (the MIT translation) fully retyped in shiny LaTeX with a few corrections and improvements to figures. A free copy of which is available here (trivia: Zuse’s name was used in the Tron: Legacy film (2010) certainly inspired by his mind blowing ideas on a digital universe).

The book also includes a panel discussion transcription on the volume topic, featuring worldwide experts including a Nobel prize in quantum mechanics, physics, cognition, computation and algorithmic complexity. In this section I asked authors (and other authors asked as well) what I thought an informed reader would ask them (including myself), sometimes leading to quite heated exchanges.

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.

**Free sample chapter(s)**

Foreword (533 KB)

Chapter 1: Introduction the Computable Universe (476 KB) by myself.

**Table of 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 toEmbodied 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)*

- Origins of Digital Computing: Alan Turing, Charles Babbage, & Ada Lovelace
*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)*

- Reaction Systems: A Natural Computing Approach to the Functioning of Living Cells
*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)*

- Information-Theoretic Teleodynamics in Natural and Artificial Systems
*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 ?ukowski)* - The Contextual Computer
*(A Cabello)* - A Gödel-Turing Perspective on Quantum States Indistinguishable from Inside
*(T Breuer)* - When Humans Do Compute Quantum
*(P Zizzi)*

- What is Computation? (How) Does Nature Compute?
*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)*

- Open Discussion on
*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)*

- What is Computation? (How) Does Nature Compute?
*Zuse’s Calculating Space:*- Calculating Space (
*Rechnender Raum*)*(K Zuse)* *Afterword to Konrad Zuse’s Calculating Space (A German & H Zenil)*

- Calculating Space (

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