The mathematical structure of innovation

We study a simple model for the evolution of the cost (or more generally the performance) of a technology or production process. The technology can be decomposed into $n$ components, each of which interacts with a cluster of $d-1$ other, dependent components. Innovation occurs through a series of trial-and-error events, each of which consists of randomly changing the cost of each component in a cluster, and accepting the changes only if the total cost of the entire cluster is...

Which technological linkages affect the sector's ability to innovate? How do these effects transmit through the technology space? This paper answers these two key questions using novel methods of text mining and network analysis. We examine technological interdependence across sectors over a period of half a century (from 1976 to 2021) by analyzing the text of 6.5 million patents granted by the United States Patent and Trademark Office (USPTO), and applying network analysis t...

Innovation and obsolescence describe dynamics of ever-churning and adapting social and biological systems, concepts that encompass field-specific formulations. We formalize the connection with a reduced model of the dynamics of the "space of the possible" (e.g. technologies, mutations, theories) to which agents (e.g. firms, organisms, scientists) couple as they grow, die, and replicate. We predict three regimes: the space is finite, ever growing, or a Schumpeterian dystopia i...

The quest for historically impactful science and technology provides invaluable insight into the innovation dynamics of human society, yet many studies are limited to qualitative and small-scale approaches. Here, we investigate scientific evolution through systematic analysis of a massive corpus of digitized English texts between 1800 and 2008. Our analysis reveals great predictability for long-prevailing scientific concepts based on the levels of their prior usage. Interesti...

Most explanations of economic growth are based on knowledge spillovers, where the development of some technologies facilitates the enhancement of others. Empirical studies show that these spillovers can have a heterogeneous and rather complex structure. But, so far, little attention has been paid to the consequences of different structures of such cross-technology interactions: Is economic development more easily fostered by homogenous or heterogeneous interactions, by uni- o...

This study here suggests a classification of technologies based on taxonomic characteristics of interaction between technologies in complex systems that is not a studied research field in economics of technical change. The proposed taxonomy here categorizes technologies in four typologies, in a broad analogy with the ecology: 1) technological parasitism is a relationship between two technologies T1 and T2 in a complex system S where one technology T1 benefits from the interac...

A key challenge when trying to understand innovation is that it is a dynamic, ongoing process, which can be highly contingent on ephemeral factors such as culture, economics, or luck. This means that any analysis of the real-world process must necessarily be historical - and thus probably too late to be most useful - but also cannot be sure what the properties of the web of connections between innovations is or was. Here I try to address this by designing and generating a set...

Technology is a complex system, with technologies relating to each other in a space that can be mapped as a network. The technology network's structure can reveal properties of technologies and of human behavior, if it can be mapped accurately. Technology networks have been made from patent data, using several measures of proximity. These measures, however, are influenced by factors of the patenting system that do not reflect technologies or their proximity. We introduce a me...

We provide a theoretical framework to understand when firms may benefit from exploiting previously abandoned technologies and brands. We model for the long run process of innovation, allowing for sustainable diversity and comebacks of old brands and technologies. We present two extensions to the logistic and Lotka-Volterra equations, which describe the diffusion of an innovation. First, we extend the short-term competition to a long-term process characterized by a sequence of...

Few attempts have been proposed in order to describe the statistical features and historical evolution of the export bipartite matrix countries/products. An important standpoint is the introduction of a products network, namely a hierarchical forest of products that models the formation and the evolution of commodities. In the present article, we propose a simple dynamical model where countries compete with each other to acquire the ability to produce and export new products....