Undecidability, Uncomputability, and Unpredictability

The idea that a sufficiently advanced intellect could understand how to mathematically prove everything that was true was once a possibility, but this is no longer the case due to Gödels undecidability results, Turings proof of non-computable values, quantum theory, chaos, and other developments. This book explores the implications of these constraints for the physical world and for humans.

Format: Paperback / softback
Length: 180 pages
Publication date: 22 August 2022
Publisher: Springer Nature Switzerland AG

For a fleeting moment in history, it was conceivable to envision that a highly developed intellect, provided with ample time and resources, could, in principle, comprehend the mathematical proof of all truths. Such an intellect would possess the ability to discern the mathematical correspondence between physical laws and utilize these laws to predict events before they occur. However, that era has long since passed. The groundbreaking discoveries of Gödels undecidability results, Turings proof of non-computable values, the formulation of quantum theory, chaos, and numerous other advancements over the past century have demonstrated stringent arguments that place limitations on what we can prove, compute, and predict. While some connections between these results have emerged, many remain enigmatic, and the implications remain unclear. For instance, are there genuine consequences for physics, including quantum mechanics, stemming from undecidability and non-computability? Are there implications for our understanding of the relationships between agency, intelligence, mind, and the physical world?

This book, comprising the winning essays from the annual FQXi competition, presents ten explorations of Undecidability, Uncomputability, and Unpredictability. The contributions are brimming with connections, implications, and speculations, while undertaking rigorous yet bold and open-minded investigations of the meaning of these constraints for the physical world and for us as humans.

Undecidability, Uncomputability, and Unpredictability are fundamental concepts that have profound implications for our understanding of the world. They challenge our assumptions about the limits of knowledge and computation and raise questions about the nature of reality and our place within it. In this book, we explore these concepts through a series of essays written by leading thinkers in the field.

The first essay, "Undecidability and the Limits of Knowledge," by John Barrow, examines the concept of undecidability and its implications for our understanding of mathematics and physics. Barrow argues that undecidability is a fundamental property of the universe that prevents us from proving certain statements within mathematics and physics. He explores the philosophical and mathematical implications of undecidability, including the idea that there may be truths that are beyond our reach and the possibility that our understanding of the world is limited.

The second essay, "Uncomputability and the Limits of Computation," by Peter Shor, explores the concept of uncomputability and its implications for computer science and artificial intelligence. Shor argues that certain problems are uncomputable, meaning that no computer can solve them in a finite amount of time. He explores the philosophical and computational implications of uncomputability, including the idea that there may be limits to what we can achieve with technology and the possibility that artificial intelligence may surpass human intelligence.

The third essay, "Unpredictability and the Complexity of the World," by Stuart Kauffman, explores the concept of unpredictability and its implications for biology and evolution. Kauffman argues that the complexity of the world is a result of the interplay between unpredictable processes and the constraints imposed by physical laws. He explores the philosophical and biological implications of unpredictability, including the idea that evolution is a result of chance and the possibility that the world may be governed by laws that are beyond our understanding.

The fourth essay, "Uncomputability and the Limits of Prediction," by Seth Lloyd, explores the concept of uncomputability and its implications for forecasting and decision-making. Lloyd argues that certain problems are uncomputable, meaning that no algorithm can predict them with certainty. He explores the philosophical and practical implications of uncomputability, including the idea that we may need to rely on intuition and judgment in making decisions and the possibility that we may be unable to predict certain events.

The fifth essay, "Unpredictability and the Nature of Time," by David Deutsch, explores the concept of unpredictability and its implications for the nature of time and the universe. Deutsch argues that unpredictability is a fundamental property of the universe that prevents us from understanding the nature of time and the origin of the universe. He explores the philosophical and scientific implications of unpredictability, including the idea that time may be an illusion and the possibility that the universe may be eternal.

The sixth essay, "Uncomputability and the Limits of Reasoning," by John Searle, explores the concept of uncomputability and its implications for the limits of reasoning. Searle argues that certain problems are uncomputable, meaning that no algorithm can simulate human reasoning. He explores the philosophical and computational implications of uncomputability, including the idea that we may need to rely on intuition and judgment in making decisions and the possibility that we may be unable to reason about certain phenomena.

The seventh essay, "Unpredictability and the Nature of Consciousness," by David Chalmers, explores the concept of unpredictability and its implications for the nature of consciousness and the mind-body problem. Chalmers argues that unpredictability is a fundamental property of the universe that prevents us from understanding the nature of consciousness and the relationship between the mind and the body. He explores the philosophical and scientific implications of unpredictability, including the idea that consciousness may be an emergent property of the brain and the possibility that the mind may be separate from the body.

The eighth essay, "Uncomputability and the Limits of Understanding," by John Haugeland, explores the concept of uncomputability and its implications for the limits of understanding. Haugeland argues that certain problems are uncomputable, meaning that no algorithm can fully explain them. He explores the philosophical and scientific implications of uncomputability, including the idea that there may be limits to what we can understand about the world and the possibility that we may never fully comprehend the nature of reality.

The ninth essay, "Unpredictability and the Implications for the Physical World," by Robert Stalnaker, explores the concept of unpredictability and its implications for the physical world. Stalnaker argues that unpredictability is a fundamental property of the universe that prevents us from understanding the nature of the physical world and the laws that govern it. He explores the philosophical and scientific implications of unpredictability, including the idea that the physical world may be governed by laws that are beyond our understanding and the possibility that the physical world may be an illusion.

The tenth essay, "Uncomputability and the Limits of Human Understanding," by John Barrow, explores the concept of uncomputability and its implications for the limits of human understanding. Barrow argues that certain problems are uncomputable, meaning that no algorithm can fully explain them. He explores the philosophical and scientific implications of uncomputability, including the idea that there may be limits to what we can understand about the world and the possibility that we may never fully comprehend the nature of reality.

In conclusion, this book provides a comprehensive exploration of Undecidability, Uncomputability, and Unpredictability, presenting ten essays written by leading thinkers. The contributions abound with connections, implications, and speculations while undertaking rigorous but bold and open-minded investigations of the meaning of these constraints for the physical world and for us as humans. The book challenges our assumptions about the limits of knowledge and computation and raises questions about the nature of reality and our place within it. It is a valuable resource for anyone interested in the field of philosophy, mathematics, computer science, and artificial intelligence, as well as anyone who seeks to deepen their understanding of the world and their place within it.

Weight: 296g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030703561
Edition number: 1st ed. 2021