Book: "The Once and Future Turing - Computing the World"

Editors: S. Barry Cooper and Andrew Hodges

Publisher: Cambridge University Press

Publication Date: During the Turing Centenary - mid 2012

Level of presentation:

Will take Scientific American articles as a model, but allow more mathematical expressions than Scientific American does. Pictures and diagrams would be welcome. The volume will be written by world-leading experts, but be relatively accessible and informative to both experts and non-experts. Contributions expressing a contemporary viewpoint on topics and areas influenced by Turing are encouraged.

Outline of contents:

General preface
Artificial intelligence / philosophy of Mind
Computability in mathematics and logic
Number theory and the Riemann hypothesis
Beyond computability in mathematics and physics
Quantum mechanics in computing, complexity and cryptology
Emergence in nature

Notes, and invited contributors, for each section:

Should contain a general introduction, containing background, history, and introducing the authors and their contributions
Andrew Hodges: Introduction
The structure of contributions should emphasise that Turing advocated both top-down and bottom-up approaches to AI.
Douglas Hofstadter: Dull Rigid Human Meets Ace Mechanical Translator - A Dialogue in Honor of Alan Mathison Turing by Douglas Richard Hofstadter

Christof Teuscher: Designed versus Intrinsic Computation
Contributors:
Martin Davis: Algorithms, Equations, and Logic

Solomon Feferman and S. Barry Cooper: Turing's `Oracle' Revisited: From Absolute to Relative Computability - and Back

Martin Hyland: The Forgotten Turing
This section might also have some very interesting things to say about more general use of computation in pure mathematical research, in ways that were totally impossible in Turing's time, but where he was a pioneer.
Andrew Booker: Turing and the Primes
The Riemann Hypothesis, what Turing did and what computation can now achieve. With some examples of other current number-theoretic conjectures, plus some plots and illustrations of prime number distribution etc.

Should explore the question what logicians now see as the role of logic in understanding the world, as reflected in the whole book. A big topic.
S. Barry Cooper: Computing in an Incomputable World
An overview of logical approaches to computability in the real world. Will look at the delicate balance between mathematical structure and embodied computation in various contexts.

Roger Penrose: On Attempting to Model the Mathematical Mind

Philip Welch: Turing Transcendent: Beyond the Event Horizon
A topic which leads into complexity theory, P/NP etc.
Scott Aaronson: tba

Ueli Maurer: Cryptography and Computation after Turing
Discussion of some modern topics in cryptography and information theory in relation to Turing's work.
This piece might also touch on the whole emergent question of synthetic life and the relationship between morphogenesis and evolutionary theory.
Richard Gordon: Walking the Tightrope: the Dilemma of Hierarchical Instabilities in Morphogenesis

Stuart Kauffman: Answering Descartes: Beyond Turing
An open quantum information processing system that is also in 'Poised Realm', and exhibits classical behavior: a Trans-Turing system that is not algorithmic. New physics, arising for open quantum systems, including both decoherence, the quantum AntiZeno effect as confirmed experimentally, and more recently REcoherence from classical behavior back to quantum coherent behavior. Relevance to theories of brain function.
Philip Maini, Thomas Woolley, Eamonn Gaffney and Ruth Baker: Turing's Theory of Biological Pattern Formation
A brief introduction to pattern formation. Turing's model - Its predictions and ideas that emerge; developmental constraints. Examples where the model is consistent with experiment. Examples where it is not. Present day applications. Other models proposed.

Stephen Wolfram: What Turing Might Have Discovered