Geometrics of the Adjacent Possible: Harvesting Values at the Curvature

Abstract: Novelty alone is not sufficient for innovation. For new ideas and products to thrive, they must find their place within the existing societal fabric, such as institutions, conventions, and infrastructures that have been built over time. Past successes create inertia, favoring conservative advances. Here, we develop a quantitative framework to map the contours of the adjacent possible in the presence of the power of typicality. Typical assemblies, frequently combined building blocks in past innovations, compress and curve the space of possibilities toward what is imaginable, accessible, and implementable, much like gravitational forces on new ideas and actions. We demonstrate that these curvatures in the space of possibilities are not just abstract constructs but empirically measurable through two complementary studies. We first show that Edison's inventions are primarily located in areas of high curvature, aligning with his strategy of building upon institutionalized domains. In contrast, Tesla's inventions are mainly found in low-curvature areas, indicating his propensity for exploring new territories and pushing innovation boundaries. Further analysis of the entire U.S. patent database reveals that innovations in high-curvature areas are more likely to yield monetary value. High-curvature areas indicate windows of opportunity through the interplay between innovation and convention, explaining why commercially successful ideas often emerge at the fringes of institutionalized domains.