A computable universe: understanding and exploring nature as computation

Foreword / R. Penrose

Preface

Acknowledgements

1. Introducing the Computable Universe / H. Zenil

Historical, Philosophical & Foundational Aspects of Computation

2. Origins of Digital Computing: Alan Turing, Charles Babbage, & Ada Lovelace / D. Swade

3. Generating, Solving and the Mathematics of Homo Sapiens. E. Post's Views on Computation / L. De Mol

4. Machines / R. Turner

5. Effectiveness / N. Dershowitz / E. Falkovich

6. Axioms for Computability: Do They Allow a Proof of Church's Thesis? / W. Sieg

7. The Mathematician's Bias and the Return to Embodied Computation / S. B. Cooper

8. Intuitionistic Mathematics and Realizability in the Physical World / A. Bauer

9. What is Computation? Actor Model versus Turing's Model / C. Hewitt

Computation in Nature & the Real World

10. Reaction Systems: A Natural Computing Approach to the Functioning of Living Cells / A. Ehrenfeucht / J. Kleijn / M. Koutny / G. Rozenberg

11. Bacteria, Turing Machines and Hyperbolic Cellular Automata / M. Margenstern

12. Computation and Communication in Unorganized Systems / C. Teuscher

13. The Many Forms of Amorphous Computational Systems / J. Wiedermann

14. Computing on Rings / G. J. Martínez / A. Adamatzky / H. V. McIntosh

15. Life as Evolving Software / G. J. Chaitin

16. Computability and Algorithmic Complexity in Economics / K. V. Velupillai / S. Zambelli

17. Blueprint for a Hypercomputer / F. A. Doria

Computation & Physics & the Physics of Computation

18. Information-Theoretic Teleodynamics in Natural and Artificial Systems / A. F. Beavers / C. D. Harrison

19. Discrete Theoretical Processes (DTP) / E. Fredkin

20. The Fastest Way of Computing All Universes / J. Schmidhuber

21. The Subjective Computable Universe / M. Hutter

22. What Is Ultimately Possible in Physics? / S. Wolfram

23. Universality, Turing Incompleteness and Observers / K. Sutner

24. Algorithmic Causal Sets for a Computational Spacetime / T. Bolognesi

25. The Computable Universe Hypothesis / M. P. Szudzik

26. The Universe is Lawless or "Pantôn chrêmatôn metron anthrôpon einai" / C. S. Calude / F. W. Meyerstein / A. Salomaa

27. Is Feasibility in Physics Limited by Fantasy Alone? / C. S. Calude / K. Svozil

The Quantum, Computation & Information

28. What is Computation? (How) Does Nature Compute? / D. Deutsch

29. The Universe as Quantum Computer / S. Lloyd

30. Quantum Speedup and Temporal Inequalities for Sequential Actions / M. Zukowski

31. The Contextual Computer / A. Cabello

32. A Gödel-Turing Perspective on Quantum States Indistinguishable from Inside / T. Breuer

33. When Humans Do Compute Quantum / P. Zizzi

Open Discussion Section

34. Open Discussion on A Computable Universe / A. Bauer / T. Bolognesi / A. Cabello / C. S. Calude / L. De Mol / F. Doria / B. Fredkin / C. Hewitt / M. Hutter / M. Margenstern / K. Svozil / M. Szudzik / C. Teuscher / S. Wolfram / H. Zenil

Live Panel Discussion (transcription)

35. 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

Zusc's Calculating Space

36. Calculating Space (Rechnender Raum) / K. Zuse

Afterword to Konrad Zuse's Calculating Space / A. German / H. Zenil

Index