Chapter 1: Computation
The Emperor's New Mind is the first chapter of the book and it focuses on the concept of computation. In this chapter, the author, Roger Penrose, explains the power of computation and the difficulty of being able to use it outside of the context of mathematics. To demonstrate, the author spends much of the chapter discussing the Turing Machine as an example of a computer that can be used to solve mathematical problems. He then goes on to explain how certain operations that can be performed with a Turing Machine can also be done with other computers. Penrose then concludes the chapter by describing the concept of "universal" or "general-purpose" computation and how it differs from the task-specific computations used in the Turing Machine.
Chapter 2: Thinking
The second chapter explores the concept of thinking and the challenges associated with attempting to understand it. Penrose begins by discussing the difficulty of accurately simulating "natural" intelligence with computers. He then proceeds to consider the notion of "universal thought" and methods for determining how such thought can be achieved. This is followed by a discussion of the various methods by which intelligence can be tested, such as the Turing Test, as well as the potential difficulties of such tests. The chapter concludes by introducing the reader to the concept of Gödel's Incompleteness Theorem.
Chapter 3: Concepts
In this chapter, Penrose explores the concept of concepts and how they relate to the world of computing. He begins by considering the concept of causation and the causal implications of certain phenomena. He then moves on to discuss the concept of abstractions and their implications for understanding the world. He spends much of the chapter discussing how concepts like numbers, sets, and other abstractions can be used to understand the world. He concludes the chapter by discussing the implications of Gödel's Incompleteness Theorem and the fact that no computer can determine the truth or falsehood of a statement.
Chapter 4: The Brain
In this chapter, Penrose dives into the world of neuroscience. He begins by discussing how the brain works, including its structure, various components, and how these components interact to produce cognitive functions. He then moves into an in-depth discussion of the various kinds of neuronal pathways and how they contribute to the processing of information. He concludes the chapter by discussing the implications of neuroscience for computing and the implications of computing for neuroscience.
Chapter 5: Intelligence
The fifth chapter of the book explores the concept of intelligence, beginning with the theory of mind. Penrose considers the notion of thought and consciousness and how these concepts can be used to explain intelligence. He then moves into a discussion of the various tests that can be used to measure intelligence, such as the Turing Test and the Stanford-Binet Intelligence Test. Finally, the chapter explores the implications of artificial intelligence and the potential risks and dangers of AI research.
Chapter 6: Universality
The sixth and final chapter of the book discusses the concept of universality and how it applies to the world of computing. Penrose considers the various methods by which a computer can be programmed to solve problems and he explains the difficulties associated with using general-purpose computers to solve problems using simulation or emulation. He then wraps up the chapter by discussing the implications of universal computation for science and philosophy. He concludes the chapter by making the case that the development of a new kind of universal computer could drastically change the way in which we approach and understand the world.
