Researchers from Queen Mary University of London have mathematically modelled the very act of ‘innovation’.
The study, published in Physical Review Letters, introduces a new mathematical framework that correctly reproduces the rate at which novelties emerge in real systems, known as Heaps’ law, and can explain why discoveries are strongly correlated and often come in clusters.
Lead author Professor Vito Latora, from Queen Mary’s School of Mathematical Sciences, said: “Studying the processes through which innovations arise can help understanding the main ingredients behind a winning idea, a breakthrough technology or a successful commercial activity, and is fundamental to devise effective data-informed decisions, strategies, and interventions to nurture the success and sustainable growth of our society.”
The team say that studying creative processes and understanding how innovations arise and how novelties can trigger further discoveries could lead to effective interventions to nurture the success of future attempts. Empirical findings have shown that the way in which novelties are discovered follows similar patterns in a variety of different contexts including science, arts, and technology.
In the study, the discovery process is modelled as a particular class of random walks, named ‘reinforced’ walks, on an underlying network of relations among concepts and ideas. An innovation corresponds to the first visit to a site of the network, and every time a walker moves from a concept to another, such association (an ‘edge’ in the network) is reinforced so that it will be used more frequently in the future. The researchers named this the 'edge-reinforced random walk' model.
To show how the model works in a real case, they also constructed a dataset of 20 years of scientific publications in different disciplines, such as astronomy, ecology, economics and mathematics to analyse the appearance of new concepts. This showed that, despite its simplicity, the edge-reinforced random walk model is able to reproduce how knowledge grows in modern science.