The science of the new

This book offers a unified quantitative framework for understanding the dynamics of novelty and innovation across biological, technological, and societal systems. It explores how first-time occurrences—ranging from everyday experiences to groundbreaking discoveries—can lead to subsequent breakthroughs. The content is organized into three main parts. The first part introduces essential theoretical tools for investigating the emergence of new ideas. The second part examines both classical and modern models that capture the evolution, interaction, and competition of innovations within complex systems. This section emphasizes the importance of models based on the concept of the "Adjacent Possible," i.e., all those things — ideas, molecules, technologies — that are one step away from what actually exists. The final section presents empirical case studies that utilize computational and data-driven methods to uncover hidden patterns in the diffusion of novelty. A postface summarizes the main findings and provides insight into future directions for research. By synthesizing insights from theoretical and computational physics, complexity science, and social sciences, this work challenges traditional views on predictability and control. It demonstrates that the forces driving innovation are both serendipitous and systematic, offering new perspectives on how progress unfolds. This comprehensive approach provides valuable methodologies for researchers, students, practitioners, and the general public, making it an essential resource for anyone looking to understand the complex processes that shape our ever-evolving world.