TABLE OF CONTENTS

**Foreword** [PDF]

Sir Roger Penrose

Preface

Acknowledgements

1.** Introducing the Computable Universe** [PDF]

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.** Information-Theoretic Teleodynamics in Natural and Artificial Systems**

A. Beavers & C. Harrison

11.** Reaction Systems: A Natural Computing Approach to the Functioning of Living Cells**

A. Ehrenfeucht, J. Kleijn, M. Koutny & G. Rozenberg

12.** Bacteria, Turing machines and Hyperbolic Cellular Automata**

M. Margenstern

13.** Computation and Communication in Unorganized Systems**

C. Teuscher

14. **The Many Forms of Amorphous Computational Systems**

J. Wiedermann

15.** Computing on Rings**

G.J. Martinez, A. Adamatzky & H.V. McIntosh

16. **Life as Evolving Software**

G.J. Chaitin

17.** Computability and Algorithmic Complexity in Economics**

K.V. Velupillai & S. Zambell

18.** Blueprint for a Hypercomputer**

F.A. Doria

*Computation & Physics & the Physics of Computation*

19. **Discrete Theoretical Processes (DTP)**

Ed 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 "Panton chrematon metron anthropon 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 Goedel-Turing Perspective on Quantum States Indistinguishable from Inside**

T. Breuer

33. **When Humans Do Compute Quantum**

P. Zizzi

Open Discussion Section

34. **Open Discussion**

A. Bauer, T. Bolognesi, A. Cabello, C.S. Calude, L. De Mol, F. Doria, Ed Fredkin, C. Hewitt, M. Hutter, M. Margenstern, K. Svozil, M. Szudzik, C. Teuscher, S. Wol- fram & H. Zenil

Live Panel Discussion (transcription)

35. **What is Computation? (How) Does Nature Compute?**

C.S. Calude, G.J. Chaitin, Ed Fredkin, T.J. Leggett, R. de Ruyter, T. Toffoli & S. Wolfram

Zuse's Calculating Space

36. **Calculating Space (Rechnender Raum)** [PDF]

K. Zuse

**Afterword to Konrad Zuse's Calculating Space** [PDF]

A. German & H. Zenil