The mathematical structure of innovation

Technological parasitism is a new theory to explain the evolution of technology in society. In this context, this study proposes a model to analyze the interaction between a host technology (system) and a parasitic technology (subsystem) to explain evolutionary pathways of technologies as complex systems. The coefficient of evolutionary growth of the model here indicates the typology of evolution of parasitic technology in relation to host technology: i.e., underdevelopment, ...

The paper reviews two prominent approaches for the measurement of technological complexity: the method of reflection and the assessment of technologies' combinatorial difficulty. It discusses their central underlying assumptions and identifies potential problems related to these. A new measure of structural complexity is introduced as an alternative. The paper also puts forward four stylized facts of technological complexity that serve as benchmarks in an empirical evaluation...

One new thing often leads to another. Such correlated novelties are a familiar part of daily life. They are also thought to be fundamental to the evolution of biological systems, human society, and technology. By opening new possibilities, one novelty can pave the way for others in a process that Kauffman has called "expanding the adjacent possible". The dynamics of correlated novelties, however, have yet to be quantified empirically or modeled mathematically. Here we propose...

In this work we analyze how reputation-based interactions influence the emergence of innovations. To do so, we make use of a dynamic model that mimics the discovery process by which, at each time step, a pair of individuals meet and merge their knowledge to eventually result in a novel technology of higher value. The way in which these pairs are brought together is found to be crucial for achieving the highest technological level. Our results show that when the influence of r...

Innovation or the creation and diffusion of new material, social and cultural things in society has been widely studied in sociology and across the social sciences, with investigations sufficiently diverse and dispersed to make them unnavigable. This complexity results from innovation's importance for society, but also the fundamental paradox underlying innovation science: When innovation becomes predictable, it ceases to be an engine of novelty and change. Here we review inn...

The notion of the "adjacent possible" has been advanced to theorize the generation of novelty across many different research domains. This study is an attempt to examine in what way the notion can be made empirically useful for innovation studies. A theoretical framework is construed based on the notion of innovation a search process of recombining knowledge to discover the "adjacent possible". The framework makes testable predictions about the rate of innovation, the distrib...

In this work, we introduce an extremely general model for a collection of innovation processes in order to model and analyze the interaction among them. We provide theoretical results, analytically proven, and we show how the proposed model fits the behaviors observed in some real data sets (from Reddit and Gutenberg). It is worth mentioning that the given applications are only examples of the potentialities of the proposed model and related results: due to its abstractness a...

We develop a new framework for modeling innovation networks which evolve over time. The nodes in the network represent firms, whereas the directed links represent unilateral interactions between the firms. Both nodes and links evolve according to their own dynamics and on different time scales. The model assumes that firms produce knowledge based on the knowledge exchange with other firms, which involves both costs and benefits for the participating firms. In order to increas...

The relationship of scientific knowledge development to technological development is widely recognized as one of the most important and complex aspects of technological evolution. This paper adds to our understanding of the relationship through use of a more rigorous structure for differentiating among technologies based upon technological domains (defined as consisting of the artifacts over time that fulfill a specific generic function using a specific body of technical know...

The web of relations linking technological innovation can be fairly described in terms of patent citations. The resulting patent citation network provides a picture of the large-scale organization of innovations and its time evolution. Here we study the patterns of change of patents registered by the US Patent and Trademark Office (USPTO). We show that the scaling behavior exhibited by this network is consistent with a preferential attachment mechanism together with a Weibull...