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: Hardback
Length: 180 pages
Publication date: 21 August 2021
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 into 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. By exploring these topics, this book offers a valuable perspective on the current state of scientific inquiry and provides insights into the future of theoretical physics and philosophy.

Weight: 438g
Dimension: 160 x 242 x 19 (mm)
ISBN-13: 9783030703530
Edition number: 1st ed. 2021