The mathematical structure of innovation

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...

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...

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...

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...

Theories of scientific and technological change view discovery and invention as endogenous processes, wherein prior accumulated knowledge enables future progress by allowing researchers to, in Newton's words, "stand on the shoulders of giants". Recent decades have witnessed exponential growth in the volume of new scientific and technological knowledge, thereby creating conditions that should be ripe for major advances. Yet contrary to this view, studies suggest that progress ...

A fundamental problem in technological studies is how to measure the evolution of technology. The literature has suggested several approaches to measuring the level of technology (or state-of-the-art) and changes in technology. However, the measurement of technological advances and technological evolution is often a complex and elusive topic in science. The study here starts by establishing a conceptual framework of technological evolution based on the theory of technological...