The mathematical structure of innovation

This paper outlines a framework for the study of innovation that treats discoveries as additions to evolving networks. As inventions enter they expand or limit the reach of the ideas they build on by influencing how successive discoveries use those ideas. The approach is grounded in novel measures of the extent to which an innovation amplifies or disrupts the status quo. Those measures index the effects inventions have on subsequent uses of prior discoveries. In so doing, the...

Novelty is not a sufficient condition for innovation. For new ideas and products to succeed, they must be integrated into the collective understanding and existing infrastructure, illustrating how the past determines the future. Here, we develop a comprehensive framework to understand how the structure of accumulated past successes curves the adjacent possible trajectory of future innovations. We observe that certain technological building blocks, upon frequent combination, c...

This work demonstrates the application of a birth-death Markov process, inspired by radioactive decay, to capture the dynamics of innovation processes. Leveraging the Bass diffusion model, we derive a Gompertz-like function explaining the long-term innovation trends. The validity of our model is confirmed using citation data, Google trends, and a recurrent neural network, which also reveals short-term fluctuations. Further analysis through an automaton model suggests these fl...

This study examines the network of supply and use of significant innovations across industries in Sweden, 1970-2013. It is found that 30% of innovation patterns can be predicted by network stimulus from backward and forward linkages. The network is hierarchical, characterized by hubs that connect diverse industries in closely knitted communities. To explain the network structure, a preferential weight assignment process is proposed as an adaptation of the classical preferenti...

Innovation, typically spurred by reusing, recombining, and synthesizing existing concepts, is expected to result in an exponential growth of the concept space over time. However, our statistical analysis of TechNet, which is a comprehensive technology semantic network encompassing over four million concepts derived from patent texts, reveals a linear rather than exponential expansion of the overall technological concept space. Moreover, there is a notable decline in the origi...

We define a novel quantitative strategy inspired by the ecological notion of nestedness to single out the scale at which innovation complexity emerges from the aggregation of specialized building blocks. Our analysis not only suggests that the innovation space can be interpreted as a natural system in which advantageous capabilities are selected by evolutionary pressure, but also that the emerging structure of capabilities is not independent of the scale of observation at whi...

We show that the space in which scientific, technological and economic developments interplay with each other can be mathematically shaped using pioneering multilayer network and complexity techniques. We build the tri-layered network of human activities (scientific production, patenting, and industrial production) and study the interactions among them, also taking into account the possible time delays. Within this construction we can identify which capabilities and prerequis...

The growth of science and technology is a recombinative process, wherein new discoveries and inventions are built from prior knowledge. Yet relatively little is known about the manner in which scientific and technological knowledge develop and coalesce into larger structures that enable or constrain future breakthroughs. Network science has recently emerged as a framework for measuring the structure and dynamics of knowledge. While helpful, existing approaches struggle to cap...

Functional technical performance usually follows an exponential dependence on time but the rate of change (the exponent) varies greatly among technological domains. This paper presents a simple model that provides an explanatory foundation for these phenomena based upon the inventive design process. The model assumes that invention - novel and useful design- arises through probabilistic analogical transfers that combine existing knowledge by combining existing individual op...

Novelties are part of our daily lives. We constantly adopt new technologies, conceive new ideas, meet new people, experiment with new situations. Occasionally, we as individuals, in a complicated cognitive and sometimes fortuitous process, come up with something that is not only new to us, but to our entire society so that what is a personal novelty can turn into an innovation at a global level. Innovations occur throughout social, biological and technological systems and, th...