The Incomputable: Journeys Beyond the Turing Barrier

Part I, Challenging Turing: Extended Models of Computation.- Ivan Soskov: A Life in Computability.- Physical Logic.- From Quantum Foundations via Natural Language Meaning to a Theory of Everything.- Part II, The Search for "Natural" Examples of Incomputable Objects.- Some Recent Research Directions in the Computably Enumerable Sets.- Uncomputability and Physical Law.- Algorithmic Economics: Incomputability, Undecidability and Unsolvability in Economics.- Part III, Mind, Matter and Computation.- Is Quantum Physics Relevant for Life?.- Trouble with Computation: A Refutation of Digital Ontology.- Part IV, The Nature of Information: Complexity and Randomness.- Complexity Barriers as Independence.- Quantum Randomness: From Practice to Theory and Back.- Calculus of Cost Functions.- Part V -- The Mathematics of Emergence and Morphogenesis.- Turing's Theory of Morphogenesis: Where We Started, Where We Are and Where We Want to Go.- Construction Kits for Biological Evolution.